Capture of thermal neutrons in 10B and 6Li: Applications in spectroscopy and in the study of weak nucleon interactions

* > * * T ~ ~ :

-

^mm^?*~--' ■. ■ ^mm^?*~--' ^mm^?*~--' . ; ^mm^?*~--' A "* ^mm^?*~--'*

TR diss

1494

10

B AND

6

Li

Applications in spectroscopy and in the study

of weak nucleon interactions

10

B AND

6

Li

Applications in spectroscopy and in the study

of weak nucleon interactions

Proefschrift

ter verkrijging van

de graad van doctor

in de technische wetenschappen

aan de Technische Hogeschool Delft,

op gezag van de Rector Magnificus

prof.dr. J.M. Dirken,

in het openbaar te verdedigen

ten overstaan van het College van Dekanen

op dinsdag 17 juni 1986

te 14.00 uur

door

Petrus Johannes Jozef Kok

doctorandus in de wis- en natuurkunde

geboren te Haarlem

TR diss "I

1494

This investigation is part of the research programme of the "Stichting voor Fundamenteel Onderzoek der Materie (FOM)" which is financially supported by the "Nederlandse organisatie voor Zuiver Wetenschappelijk Onderzoek (ZWO)".

CONTENTS B i z .

1 . GENERAL INTRODUCTION 9

1 . 1 . Neutron beam f a c i l i t i e s 9

1 . 2 . Capture gamma-ray spectroscopy 12

1 . 3 . Parity v i o l a t i o n in the ( n , a ) reaction 16

References 21

2 . INVESTIGATION OF EXCITED STATES OF 7L i BY MEANS OF THERMAL

NEUTRON CAPTURE 23

A b s t r a c t 2 3

2.1. Introduction 24

2.2. Capture of thermal unpolarized neutrons by

Li nuclei 25

2.2.1. Experimental 25

2.2.2. Gamma-ray spectrum analysis 25

2.2.3. Results 26

2.3. Lifetime of the 478 keV transition 30

2.3.1. Introduction 30

2.3.2. Fitting of the stopping power curves 30

2.3.3. Line shape 30

2 . 3 . 4 . F i n i t e target s i z e correction 35

2 . 3 . 5 . Experimental 35

2 . 3 . 6 . Conclusions 38

References 42

3 . INVESTIGATION OF EXCITED STATES OF 1 1B and 7L i BY MEANS OF

THERMAL NEUTRON CAPTURE ON 1 0B NUCLEI 4 5

A b s t r a c t 45

3.1. Introduction 47

3.2. Investigation of the

B(n,Y) reaction with unpolarized

boron nuclei 47

3.2.1. Experimental 47

3.2.2. Gamma-ray spectrum analysis 48

3.2.3. Level scheme and cross section of the

10

B(n,Y) reaction 49

Biz. 3.3. The 1 0B(n,a) reaction investigated with polarized

boron nuclei 56 3.3.1. Introduction 56 3.3.2. The target polarization 58

3.3.3. The directional distribution of the a and 7L i

particles 61 3.3.4. Discussion of the shape of the 478 keV line 64

3.3.5. The influence of the stopping power on the

478 keV line shape 65 3.3.6. Results and discussion 67

References 67

4. AN INVESTIGATION OF THE ADMIXTURE OF STRONG AND WEAK

INTER-ACTIONS IN THE 1 0B(n,a) REACTION WITH SLOW NEUTRONS 77

Abstract • 77

4.1. Introduction 78 4.2. Experimental 80 4.3. Estimate of parity violation in the 1 0B(n,a) reaction 83

4.4. Enhancement of irregular transitions by centrifugal

barrier effects 87 4.5. Conclusion 91 References 92

SAMENVATTING 95

LIST OF ABBREVIATIONS AND SYMBOLS 98

CHAPTER 1

GENERAL INTRODUCTION

The High Flux Reactor (HFR) in Petten provides powerful means to study thermal neutron capture. Nuclei absorbing low energy neutrons lose their energy excess of the order of 8 MeV almost always by the emission of Y-radiation. Recently in Petten (n,y) spectroscopy was used to study the decay of nuclei of intermediate mass 2"*Na [l, 2 ] , ^6Sc [ 3 ] , "*8'50T1 [4j 5] a n d 6t>66C u [6> 7] _ A n a c c u r a t e determination of the energies and Intensities of the transitions involved made it possible to construct fairly complete and extensive decay schemes (sometimes up to 100 levels). In this thesis the thermal capture in '°B and Li nuclei is described. Among the lighter nuclei boron and lithium are the only ones that show, besides y-radiation, a-particle emission (see fig. 1 ) . The newly acquired knowledge from the (n,ai) experiments is of value for the analysis of a parity violation experiment carried out in Petten, as will be elucidated furtheron.

1.1. Neutron beam facilities

The different measurements reported in this thesis require several experimental setups and various neutron beams. High precision in determining energies and intensities of neutron capture Y-rays, especially those of low intensity, can be achieved with a beam of thermal neutrons with high flux density and low background conditions. Therefore a system consisting of focussing nickel mirrors had been installed near the reactor core. Direct transmission of neutrons from the reactor will be prevented by the curved stack of 90 mirrors. As a consequence only totally reflected neutrons may pass the mirror system to be focussed at the target position (see fig. 2 ) . As the critical angle for total reflection decreases for increasing neutron energy the system acts as a low-pass neutron filter. Consequently, the mean neutron energy appeared to be 20 meV and the neutron flux density at the focus spot is 8 x l 01 2 m- 2 s- 1 (width: 0.15 m and height 0.01 m at the focus spot).

With a transversally polarized neutron beam it Is possible to do directional distribution measurements of neutron capture gamma-rays for

v ( S / 2 , 7 / 2 )

- - > v < l / 2 , 3 / 2 ) +

1/2"*

3 / 2

reactor

core

focus

spin investigations in the compound nucleus. For this purpose a magne-tized Heusler single crystal (Cu.MnAl) has been placed In another beam from the HFR. Neutrons are polarized by means of Bragg reflection from the (ill) plane of this crystal. As a result the diffracted neutron beam consisted mainly of a beam of first order reflected neutrons, their energy being 88 meV, with a polarization of 95%. The neutron flux density after reflection at the position of the target was 5xl09 m ~2 s- 1. As will be described in Chapter 3 the neutrons and the target nuclei are polarized along the same axis perpendicular to the beam (see Chapter 3, fig. 4 ) .

In contrast to the above-mentioned spin measurements, the parity violation experiment required longitudinally polarized neutrons. With a set of magnetized permendur mirrors polarization can be achieved by total reflection of the neutrons. Just as for the focussing nickel mirrors the direct transmission of neutrons from the reactor core has been made impossible. Total reflection is only possible for neutrons with spins parallel to the magnetization of the mirrors. In this way a focussed beam arises with a neutron polarization of 90%, and a neutron flux density of 4 X 1 01 1 m- 2 s- 1. The mean energy of the neutrons has been measured to be 15 meV. Finally the spins of the neutrons were turned into the direction of a longitudinal guide field (see Chapter 4, fig. 3 for the general setup).

1.2. Capture gamma-ray spectroscopy

In the simplest experimental situation the Y-radiation produced by excited 7Li or nB nuclei can be studied by irradiating 6L i or l QB nuclei with an unpolarized thermal neutron beam (see Chapter 2 and 3 ) . For the detection of the low-energy gammas a single high purity germanium (HPGe) detector is needed, whereas a pair spectrometer has been used for high-energy gammas. The pulses are digitized by means of an analyzer, operating in the Pulse Height Analysis mode. The accumu-lated data are put on tape, for further handling on a CDC Cyber 175 computer. From the analysis of the resulting spectra, decay schemes can be constructed (Chapters 2 and 3 ) . Comparison of the intensities of the

1 0B(n,Y) lines with calibration lines yields a cross section for this reaction, which is more accurate than known before. For primary

transi-tions the Doppler shift due to recoil is well defined. In case of light nuclei (A<20) a detectable Doppler broadening of secondary transitions due to recoil helps to distinguish between primary and secondary tran-sitions. With the 10B(n,c«Y) reaction it is even possible to use this Doppler broadening for a determination of the lifetime of the 478 keV level. Provided that the stopping power of the medium, in which the 'Li product nuclei recoil, is known, the line shape of the 478 keV transi-tion can be approximated by the so called Doppler Shift Attenuatransi-tion Method (DSA). For a perfect detector resolution and particles moving with constant velocity, the line shape will be rectangular, if there is no correlation between primary and secondary radiation (see Chapter 3 ) . By dividing the slowing-down time of the 'Li nuclei into a large number of time intervals, during each of which the 'Li nuclei are only slight-ly decelerated, the line shape can be constructed by a summation of rectangles. The width of the first rectangle will be 2(v /c) E , where c is speed of light, v the recoil velocity and E = 478 keV. Its

o Y height can be calculated from the decay law: N=N exp(-t/x), and will

o

be N -N =N [l-exp](-t / T ) ] , where T is the lifetime of the level and N is number of excited Li nuclei at time t , the end of the first time interval. Likewise at time t. a second rectangle can be constructed with width equal to 2(v /c) E and height reduced by decay equal to N -N = N [exp(-t)/t)-exp(-t / T ) ] . The velocity v depends on the stopp-ing power of the medium. In this way a histogram summation of many rectangles leads to the construction of the line shape. This summation has been visualized in figure 3. For comparison with a real line shape the peak should be convoluted with the detector resolution (see Chapter 3 for a similar procedure). In table 1 it can be seen that, if the time intervals are chosen as dt/t=dx/vT, where dx is 1 0- 7 m, then 15 rectan-gles are sufficient to represent more than 99.5% of the deexcited 7Li nuclei.

The DSA method is not useful for very short lifetimes, because in that case all the recoiling nuclei would show maximum Doppler shift. As a consequence, the resulting line shape would then be perfectly rectan-gular for an ideal detector resolution. On the other hand if the life-time is too long, all the recoil nuclei will be stopped before deexci-tation has been taken place, and then the transition will not be broad-ened. So the DSA method is only of interest in an intermediate

ENERGY

Fig.3. Construct ion of the line shape for an Ideal detector

response for the 478 UeU gammas emitted by excited

LI

nuclei, which recoil In boron. Stopping power data are

taken from Morthcl iffe 181. Intensity Is In arbitrary

units.

TABLE I

Rectangle width height time velocity deexclted

Li

number particles

(keV) (%) (t/x) (cm/s) (%)

Since thermal neutrons are captured without orbital momentum (s-wave capture) the spin values of the compound nucleus are I±l/2 (I being the spin of the target nucleus). In the case of 1 0B with 1=3 the compound spin values are 7/2 and 5/2. The fraction of the reaction that goes through the 7/2 channel is expressed by the spin admixture ratio a,.

From a nuclear orientation experiment with target polarization f1 and neutron polarization f the spin admixture ratio o and the sign of interference between both channels (see Chapter 3) can be determined from the expression:

W(0) = 1 + f ^ „ [ ( « j ^ " 1) + A ^ P ^ c o s 0)] (1)

The sign of the channel interference follows from the A- coefficient [9]. The usual method is to reverse the neutron polarization vector periodically, and to measure the difference in intensity of the capture gamma radiation between parallel and anti-parallel spin orientations. This can be achieved with two Ge(Li) detectors positioned in directions parallel and perpendicular to the polarizing field. However, the 478 keV transition is suitable for the development of a new accurate method for determining a . In Chapter 3 this method, also based on the analy-sis of the line shape, has been described. An accurate determination of this a is essential in the interpretation of the parity violation experiment described in Chapter 4, because the asymmetry in the emis-sion of the a-particles depends strongly on the fraction of the reac-tion that goes through channel spin J=5/2.

1.3. Parity violation in the (n,q) reaction

Non-conservation of parity (PNC) in weak interactions was proposed by Lee and Yang [lO]. Complete parity violation has been discovered through the B-decay of 6 0Co [ll]. In case of weak interaction between nucleons (in addition to the usual stong nuclear forces) such a viola-tion should occur just as well. As a consequence a breaking of reflec-tion symmetry can be observed in the (n,a) reacreflec-tion through pseudo-scalar quantities like f . k , where the neutron polarization f and

^ n a' n the o-particle momentum vector k are axial and polar vectors

respec-tively. In the actual admixture of strong (parity conserving) and weak interactions between nucleons, the former dominates, and pseudoscalars are only of the order 1 0 " . In some cases, however, such pseudoscalars may be amplified by structural or dynamical enhancements (see Chapter 4 for references [ l , — , 1 0 J ) .

It was proposed by Lobov and Danilyan [12j to study the weak nucleon interaction by an investigation of parity non-conservation (PNC) in the a-disintegration using polarized 6Li and 1 0B nuclei. For both nuclei the cross section is very large for the n.ct-reaction and dominates by far the thermal neutron capture Y-emission. These experiments are of special interest, because theoretical calculations are more reliable for light nuclei than for heavy nuclei. The weak contribution to the nucleon interaction may admix states which have the same angular momentum but opposite parity. With parity fully conserved only an L=3 a-component is possible between the *'B compound state (5/2, 7/2) and the excited l/2~ state of 'Li. This is denoted as the regular compo-nent. In case of parity admixture also the irregular momenta L=2 and 4 for the emission of the a-particles are allowed (see Chapter 4, figure 1 ) . Hence an asymmetry in the emission of the a-particles with respect to the direction of nuclear polarization might appear as:

W(9) = const. (1 + A f cos 8) (2) n

where f is the neutron beam polarization, and 8 the angle between polarization vector and the momentum of the a-particle. The asymmetry coefficient A has been derived theoretically in [l2j. Experimentally, the asymmetry is given by:

A

■ — — k — - — - <3>

which is a function of differences between ionization currents I for different neutron polarization direction (+ or - ) , and different parts (1 and 2) of a detector, consisting of a set of wire ionization chambers. The experimental asymmetry A can be set equal to Af <cos 8>.

This detector (see Chapter 4, fig. 2) has been developed at the In-stitute for Theoretical and Experimental Physics (ITEP) in Moscow, which has a lot of experience in determining small PNC effects in nuclear interactions [l3, 14, 1 5 ] . The Petten FOM-ECN nuclear structure group had an intense polarized neutron beam available. This made a combination of the two facilities interesting as a joint venture, that was arranged under the terms of the 1965 exchange agreement between the USSR State Committee for Atomic Energy, the Belgian Study Center for Nuclear Energy and ECN. In Chapter 4 it has been described in more detail how the detector was placed in a longitudinally polarized neutron beam at the HFR, in Petten. During the measurements the cur-rents from the individual modules are added, and converted into digital signals and stored in a 32 k multichannel analyzer (ND 66) operating in multiscanning mode. Data were accumulated at the same time for the four different gaps of the detector modules into four different Voltage Frequency Converters (VFC). With a spin flipper, a device specially developed for this purpose by the ITEP group, It is possible to quickly reverse the polarization direction of the neutron spin. The counts were registered in a channel during a fixed period (3.8 s ) , and at every spin reversal the registration continues in one higher channel number. With this spin flipper it was possible to take measurements with polarization direction of neutron spin in repeating sequences like + -- + -- + + -- or + -- + -- + -- + -- + -- . The former sequence has the - advan-tage of cancelling any possible linear asymmetry component of the setup, and has, therefore, been chosen. In order to distinquish between + or - channel the VFC's are adjusted in such a way, that the frequency during registration with neutron spin in the + polarization direction is twice that of the - polarization direction. In that way 4 spectra, consisting of 8192 channels, were filled in 8.5 hours and put on tape for further handling with a CDC Cyber 175 computer. To avoid instrumen-tal effects the longitudinal guide field is thereafter turned into the opposite direction, after which the data acquisition continues. A list of different combinations of spin and guide field is given in table 2. Software has been written to calculate the weighted mean of the spin sequences of all accumulated spectra. If for some reason the order in the spin sequence appeared to be incorrect, that spectrum was omitted In the analysis. In addition it was checked, whether the channel con

TABLE 2

Summary of the asymmetry measurements with polarized as well unpolarized neutrons.

direction of the longitudinal guide field

D-gaps B-gaps D-gaps B-gaps

'*)

*)

As a further check of the symmetry of the electronical and magnetic parts of the system, measurements have been conducted during reactor stops with a battery as input to the preamplifiers. The resulting asymmetry appeared to be better than 5 x 1 0- 9. See also Chapter IV fig. 2.

tents are normally distributed round their arithmetic mean. In Chapter 4 the results of these measurements are compared with theoretical esti-mates . The experimental development has gone in parallel with refine-ments in the theoretical analysis given in [l6], which made a good comparison possible.

Chapter 2 has been published in Nuclear Instruments and Methods [17], Chapter 3 has been accepted for publication in Zeitschrift für Physik, and Chapter 4 is based upon a paper intended to be published.

The contents of this thesis will also be available in the form of an ECN external report (ECN-184).

REFERENCES

[I] T.A.A. Tlelens, J. Kopecky, K. Abrahams, and P.M. Endt;

Nucl. Phys. A403 (1983) 13.

[2] T.A.A. Tlelens and J.B.M, de Haas;

Nucl. Phys. A425 (1984) 303.

[3] T.A.A. Tlelens, J. Kopecky, F. Stecher-Rasmussen, W. Ratynski,

K. Abrahams, and P.M. Endt;

Nucl. Phys. A376 (1982) 421.

[4] J.F.A.G. Ruyl and P.M. Endt;

Nucl. Phys. A407 (1983) 60.

[5] J.F.A.G. Ruyl, J.B.M, de Haas, P.M. Endt, and L. Zybert;

Nucl. Phys. A419 (1984) 439.

[6] M.G. Delfinl, J. Kopecky, J.B.M. de Haas, H.I. Llou, R.E. Chrien,

and P.M. Endt;

Nucl. Phys. A404 (1983) 225.

[7] M.G. Delfinl, J. Kopecky, R.E. Chrien, H.I. Liou, and P.M. Endt;

Nucl. Phys. A404 (1983) 250.

[8] L.C. Northcliffe and R.F. Schilling;

Nuclear Data Tables A7_ (1970) 223.

[9] J.J. Bosman and H. Postma;

Nucl. Instr. and Meth. 148^ (1978) 331.

[lO] T.D. Lee and C.N. Yang;

Phys. Rev. 104_ (1956) 254.

[II] C.S. Wu, E. Ambler, R.W. Hayward, D.D. Hoppes, and R.F. Hudson;

Phys. Rev. 105_ (1957) 1413.

[l2] G.A. Lobov, G.V. Danilyan;

Izv. Akad. Nauk SSSR, 41^ nr. 8 (1977) 1548.

[l3] Y.G. Abov, P.A. Krupchltsky, Y.A. Oratovsky;

Phys. Lett. 12_ (1964) 25.

[u] Y.G. Abov, P.A. Krupchitsky, M.I. Bulgakov, O.N. Ermakov,

I.L. Karpichiti;

Phys. Lett. b2_7_ (1968) 16.

[l5] Y.G. Abov, O.N. Ermakov, P.A. Krupchitsky; JETP 65_ (1973) 1738.

[16] V.E. Butiakov and V.P. Gudkov; Nucl.Phys. A401 (1983) 93.

[l7] P.J.J. Kok, K. Abrahams, H. Postma, and W.J. Hulskamp; Nucl. Instr. and Meth. B12^ (1985) 325.

CHAPTER 2

(Published in Nucl. Instr. and Meth. B)

INVESTIGATION OF EXCITED STATES OF 7Li BY MEANS OF THERMAL NEUTRON CAPTURE

P.J.J. KOK and K. ABRAHAMS

FOM-ECN Nuclear Structure Group, Energieonderzoek Centrum Nederland, Petten, The Netherlands

H. POSTMA

Lab, voor Technische Natuurkunde, T.H. Delft, Lorentzweg 1, Delft, The Netherlands

and

W.J. HUISKAMP

Kamerlingh Onnes Lab., Rijksuniversiteit Leiden, The Netherlands

ABSTRACT

Capture of unpolarized thermal neutrons has been used to gain infor-mation on the 7L i level scheme. Two reactions have been investigated. Firstly, a study has been made of the decay scheme of 7L i through the

Li(n,y)7Li reaction. Three y-transitions were observed and placed. The binding energy value of this reaction turned out to be Q » 7251.02(9) keV. Secondly, investigation of radiation from excited 7L i produced by the 10B(n,ct)7Li reaction, made it possible to deduce a more precise lifetime of the 478 keV level of 7L i ; namely x = 102 ± 5 fs. This value is compared with existing data; it agrees with previous less accurate independent values and an average could be made in order to reduce the error further. As a byproduct the analysis of the peak shape of the 478 keV transition offered a new method for estimating the size of boron grains embedded in other materials.

2.1. Introduction

This paper covers measurements on gamma radiation emitted by excited 7L i nuclei in the 6Li(n,Y)7Li and 10B(n,a)7Li reactions. The capture of thermal neutrons in lithium and boron nuclei is dominated by the (n,a) reaction. Reports on Y-spectrum measurements are scarce for L i , due to the weak (n,Y) reaction compared to the (n,a) reaction. In the case of 6Li the cross sections for the (n,a)- and (n,ï)-reactions are 940 barn, respectively 38.5 mbarn [l]. The 1 0B(n,a) and 1 0B(n,T) reac-tions have cross secreac-tions of 3837 barn and 500 mbarn. The latest (n,Y) experiments on 1 0B and 6L i were reported in 1967 by Thomas et al. [2j. A reinvestigation with improved techniques, in particular with our high-sensitivity facility for (n,"f) spectroscopy, should give more accurate results. The second part of this article reports on a measure-ment of the lifetime of the first excited state of Li, by means of the Doppler shift attenuation (DSA) method (see [3]). The lifetime can be determined from the line shape of the 478 keV transition, and the known energy loss of the recoiling 7Li nucleus as a function of its velocity. With the improved experimental equipment, and because more accurate stopping power data are available, the lifetime can now be measured with a much higher precision. Recent interest in the 478 keV level of 7L i [4,5] shows that a more precise value of the lifetime is relevant in shell model considerations. Moreover, as can be deduced from the paper of Neuwlrth [ 3 ] , the lifetime of the 478 keV level enters direct-ly into the stopping power curve also of other boron compounds [6,7]. Improved stopping power data could be of interest in heavy ion beam technology and other practical applications.

2.2. Capture of thermal unpolarlzed neutrons by 6Ll-nuclel

2121l1_Exgerimental

The gamma radiation emitted by excited lithium nuclei after thermal neutron capture, has been detected with a high purity p-type germanium

(HPGe) detector with a relative efficiency of 5%. The detector together with two Nal(Tl) crystals has been used as a pair spectrometer operat-ing in coincidence mode. In order to study low energy transitions to the ground state also a measurement has been performed with the central detector operating in single mode. Due to the competing (n,a)-reaction only 1 out of every 20,000 captured neutrons gives rise to an excited state of Li; in consequence the triple coincidence rate of the pair spectrometer was only 0.3 counts/s. Spectra were recorded during 384 h by means of an 8k Laben ADC and stored in the memory of a P9205 Philips on-line computer, which has been programmed to dump the data every 12 h on tape.

The target consists of LiF powder, containing 95.73 at% of enriched 6L i . It was encapsulated in a rectangular thin-walled teflon holder of 5x5x1 cm . Placed in a beam of unpolarized thermal neutrons from the High Flux Reactor in Petten, the target has been exposed to a flux density of 8x10° neutrons/cm2s.

2^2.2^ Gamma-ray_ S£ectrum analysis

Spectra were taken in the region between 1.5 and 10.5 MeV with a dispersion rate of 1.10 keV/channel. After correction for minor zero-point and gain shifts, the 12h spectra were summed with the aid of a CDC 175 Cyber computer. Peaks of the resulting total spectrum are fitt-ed with a gaussian curve modififitt-ed with a small asymmetry term. Back-ground lines could be determined by measuring the gamma radiation emit-ted by a dummy carbon scatterer. The most important background contri-butions are due to capture of scattered neutrons by H, Si, Fe, Cu, Ti, Cr, Al, Pb and Sb in the surroundings of the target. Other detected lines are due to the 3 5C l ( n , y ) , 1 9F(n,y) and 1 2C(n,y) reactions from impurities in the target and its holder. Strong y-rays from the 3 5Cl(n,y) reaction [8], with energies based on the 412 keV 1 9 8A u

Stan-dard, have been used for energy and intensity calibration. Also the ^ ( n . Y ) 2223 keV line, recently compared to the 1 9 8A u standard [24], has been included in the energy calibration. Errors in the y-transi-tions of Li include a systematical uncertainty of the interpolation procedure with respect to the 412 keV 19°Au standard. The energy cali-bration was obtained by means of a fourth degree polynomial fit through 15 points. The full-width-half-maximum (FWHM) of the pair spectrometer increases linearly with the square root of energy from 2.9 keV near 2.2 MeV to 5.0 keV at 7.0 MeV.

2.2.3. Results

The transitions, together with the levels also known from other reac-tions, are shown in figure 1. Our results are in agreement with mea-surements presented in [4], [ll], [l2], except that the uncertainty in the results has become one order of magnitude smaller (see table 1 ) . New transitions could not be assigned; apart from the known primary electric dipole transitions to the ground state and to the 478 keV level, and the secondary magnetic dipole transition from the 478 level to the ground state. There has been a search for the primary transi-tions to levels at 6.68 and 4.63 MeV, however they could not be traced, hence we conclude that the population probability of these levels is below 5%. This observation agrees with the spin assignments of 5/2" and 7/2" in the level scheme of Ajzenberg-Selove [ 9 ] , which indicate res-pectively magnetic quadrupole and electric octupole character for the transitions to these levels, if the capture proceeds mainly through the J = 1/2 spin channel. With J = 3/2 a 571 keV transition to the 6680 keV level could be expected. The reported value [l] of 80% capture through J = 1/2 is in accordance with the weakness of this line.

The additional experiment in the low energy region reveals, except for the 478 keV level, no new levels. The precise value of the energy of this 477.611(12) keV line had been taken from Ajzenberg-Selove [9J and is not refitted, because of the high accuracy of the value from

[9]. Since part of the 478 keV line is due to boron from the surroun-dings and because of its much bigger recoil broadening (15 k e V ) , its

Table 1 Energies E and intensities I of °Li(n,Y) gamma rays, as

measured with a pair spectrometer, and recoil corrected

ener-gies E

+ E

E

E

+

E

I E + E

Y Y r Y Y r

(keV) (keV) a) (keV)

Thomas b) Spilling c) Op den Kamp d)

7246.96(12) 7250.99(12) 62(2) 7251(2) 7249.9(8) 7250.3(9)

6769.93(15) 6773.44(15) 38(2) 6773(2) 6772.2(5)

a) A weighted mean of the present values 63(3), 37(2), and the values

from [4]

b) See [4]

c) See [ll]

d) See [12]

reaction could only be discerned as a small and narrow spike on a broad boron background peak.

For light nuclei (A < 20) it may be possible, to check the primary or secondary character of capture Y-transitions, by measuring the FWHM of the lines, because only secondary transitions will show Doppler broad-ening (see Wetzel [lOj). Inspection of the FWHM of the observed Y~peaks indicates that, except for the secondary 478 keV transition, line broadening does not occur. This is a further confirmation of the level scheme.

The recoil corrected neutron binding energy has been deduced to be 7251.02(9) keV, which should be compared with 7250.0(5) keV obtained by Spilling [ll] and with 7250.3(9) keV given by Op den Kamp [12]. The new result is a factor 5 more accurate.

4 -i

neu cm /mg

dE/dx 2

1

-0.00

0.25

0.50

0.75

1.00

-> Hew'

Fig.3. Stopping power, dE/dx, of boron and iron versus the

square root of the LI -nucleus energy, E.

where 8 is the angle between the direction of motion of the Li-nucleus and that of the photon, c is the speed of light, v is the velocity of the Li-nucleus, as a function of the time t, during which the recoiling nucleus may be decelerated by collisions. If a boron target is irradi-ated with thermal neutrons, the produced Li-nuclei will have an isotro-pic directional distribution, because the neutrons do not contribute an orbital angular momentum (1 = 0 ) . Therefore the directional distribution of the emitted photons is isotropic, and a detector will measure Doppler shifts between +(v/c)E and -(v/c)E . A construction of the broadened Y-spectrum is possible in terms of a histogram summation of rectangles. The widths of the rectangles depend on the velocity of the Li-nuclei and their heights, on the lifetime of the level, by means of the exponential decay law, as has been shown by Neuwirth et al. [ 3 ] . The detector response for radiation from the boron powder as shown in figure 4b can be well described by a function

f(x) = f (x) + f (x) + f ( x ) , (2) p b c

where x is the channel number, f(x) is a summation of the peak function f , lineair background function f, and a function f . Incident photons are scattered under a small angle inside the target or detector window (external Compton effect). This, together with insufficient charge trapping, causes an increased number of counts in the low channel re-gion near the peak, as described by f . This term depends on a step function s(x-x'), on the proportionality constants p and c, and on the channel content A(x') in the peak region, as:

fc(x) = I c.A(x').s(x-x*). I e x p ^ x1"1) - (3) x' 1

In practice five values of 1 were sufficient for a good fit.

Usually the detector response of one isolated Y_ ra y peak can be des-cribed with a Gaussian function f,, (see also [25]),

fG = 2 / ( ^ p ) A/FWHM exp {-41n2 ( x - x ^ / F W H M2) (4)

1 0sx S 4 3 -COUNT S i 1 -i 0 -N I B F3 GflS ( a )

( ~ ~~\

460

470 480

ENERGY

430

-> keU

10

X 12

BOROH POUIDER Cb>

Fig. 4. The line shape of the 478 keU gamma trans It I on

under Influence of the stopping medlumi

for BF gas (a) and boron powder (b).

folding the function representing the histogram summation of rectangles mentioned above with the detector resolution function f , the response

G

on the 478 keV broadened line can be found. After subtraction of the background f, and the asymmetric function f , this will result in

b c pictures like figures 6 and 7.

2.3.4^ Finite target_size correction

If the lifetime of the level in question is long enough a substantial part of the 7Li-nuclei may deexcite to the groundstate, while moving outside the target. This could be the case if the target consists of a powder of small sized grains, such that the recoiling nuclei are leav-ing these grains before beleav-ing stopped. The grain size must then be taken into account with respect to the spatial distribution of the 'Li-nuclei. Instead of one unique line shape expected for the emitted pho-tons in an extended boron target, the line will be a superposition of several lines, each representing a different Doppler broadened line caused by nuclei that can travel several path lengths in the boron grains.

A grain size distribution has been determined by scanning electron microscopy, resulting in a histogram as exposed in figure 5. Calcula-tions for this specimen indicated that the fraction of 7L i nuclei that can travel through more than one grain is negligible. Moreover the precise form and size of the grains is not expected to be of much influence on the line.shape.

2.3.5. Experimental

Gamma radiation emitted by a target, that was irradiated by a thermal neutron beam, was detected by the same HPGe detector as mentioned in section 2.2.1 and spectra were recorded by means of an 8k Laben ADC. The dispersion rate of the ADC had been taken at 0.44 keV per channel and the FWHM of the HPGe detector turned out to be 1.65 keV at 478 keV. The 35Cl(n,Y)-lines of an Fe.Cl, calibration source were used to calibrate for energy and line shapes of prompt "^-transitions or of secondary transitions from heavier nuclei.

fur-10 15 20

class number (I)

Fig.5. Grain size d I str Ibut I on of boron pou/der, as determined by

scannIng electron mIcroscopy.

Hbout 2300 particles have been class IfIed.

0.09

0.0G

0.03

0.00

--460

ENERGY

Fig.6. Theoretical line shapes compared with experimental points.

Calculations haue been made u i th lifetimes of 62, 102, and

142 fs. Peak areas haue been taken equal to unity.

ther tested by means of another experiment on a BFg-gas sample. The stopping power of this gas (atmospheric pressure) is too small to have any significant influence on the velocity of the recoiling 7Li-nuclel, so the Doppler shift can be calculated on basis of equation (1) with a constant velocity v. A resulting gamma spectrum will show a more rec-tangular shape (see figure 4 a ) .

If there is another transition of 483 keV in the 15 keV broad region, - as suggested by Neuwirth [3] -, this would clearly show up as an additional peak. However, the B F3 spectrum in figure 4a does not show an additional 483 keV line: its height is less than 1% of the BF3 line. In the analysis of the boron spectrum the possible existence of a 483 keV line has therefore not been accepted.

2.3.6. Conclusions

Comparison of calculated line shapes for different lifetime values with the experimental one, as demonstrated in figure 6, results in a lifetime of T = 102 ± 5 fs. Here the error results from a x2 analysis of the line shape; it includes statistical errors as well as errors in the stopping power curves. This is a value that is in good agreement with the results 106 ± 14 fs obtained by Paul et al. [l5], also a DSA measurement, and with previous resonance fluorescence measurements (see table 2 ) .

The accuracy of the experiment depends for a great deal on the stopp-ing power data. A further improvement of the accuracy in the determina-tion of T may therefore be expected, if more precise stopping power data for boron become available. It is not allowed to average DSA m e a -surements in order to reduce the error; all these mea-surements have a common systematical error from stopping power data. So our present result has been averaged only with the values obtained by resonance fluorescence, as mentioned in table 2, except for the too different value taken from [2l]. We adopt on this basis a mean lifetime of

T = 102 ± 4 fs.

Along similar lines the Ajzenberg-Selove review [23J mentions a value of 107 i 5 fs, and Paul et al. adopted a mean lifetime of 110 ± 10 f s .

Table 2 Summary of lifetime values for the 478 keV level of 'Li

ob-tained in various experiments

mean life

(fs)

75 ± 25

77 ± 8

106 ± 14

133 ± 16

110 ± 30

115 + 14

125 ± 6

93 ± 12

102 ± 5

method

DSA

DSA

DSA

DSA

RF

RF

RF

RF

DSA

reference

16

17

15

18

19

20

21

22

this work

a) DSA = Doppler shift attenuation method

RF = resonance fluorescence method

0. 10

Influence of grain size

0. In

0.05

ENERGY

Fig.7. The line shape for 2 different sizes of boron grains

embedded In Iron have been calculated.

The agreement between the various results is satisfactory, except for the value mentioned in [17J (see table 2 ) , which differs more than three standard deviations from the above mean value.

The dependence of the line shape on the grain size may be of interest in determining the distribution of boron mlcrograins embedded in other materials or in compounds of boron. As an example, figure 7 presents results for boron grains of diameters 10xl0_1* cm and O.lxlO-1* cm res-pectively embedded in solid iron or large iron grains. Again the stopp-ing power data of Northcliffe and Schillstopp-ing for boron and iron have been used. The deformation of the line shape for other stopping media would be either more or less pronounced, depending on their respective stopping power.

REFERENCES

[l] S.F. Mughabghab, M. Divadeenam, and N.E. Holden;

Neutron cross sections, vol. 1 (Academic Press, New York, 1981)

pt. A.

[2] G.E. Thomas, D.E. Blatchley, and L.M. Bollinger;

Nucl. Instr. and Meth. 5£ (1967) 325.

[3] W. Neuwirth, U. Hauser, and E. Köhn;

Z. Physik 220_ (1969) 241.

[4] N. Kumar;

Nucl. Phys. A225 (1974) 221.

[5] H.D. Knox, and R.0. Lane;

Nucl. Phys. A403 (1983) 205.

[6] W. Pietsch, U. Hauser, and W. Neuwirth;

Nucl. Instr. and Meth. 132_ (1976) 79.

[7] W. Neuwirth, W. Pietsch, K. Richter, and U. Hauser;

Z. Physik A275 (1975) 209.

[8] B. Krusche, K.P. Lieb, H. Daniel, T. von Egidy, G. Barreau,

H.G. Börner, R. Brissot, and C. Hofmeyr;

Nucl. Phys. A386 (1982) 245.

[9] F. Ajzenberg-Selove;

Nucl. Phys. A320 (1979) 1.

[lO] K.J. Wetzel;

Phys. Rev. 181^ (1969) 1465.

[ll] P. Spilling, H. Gruppelaar, H.F. de Vries, and A.M.J. Spits;

Nucl. Phys. A113 (1968) 395.

[l2] A.M.F. Op den Kamp, and A.M.J. Spits;

Nucl. Phys. A180 (1972) 569.

[13] L.C. Northcliffe, R.F. Schilling;

Nuclear Data Tables A7_ (1970) 233.

[l4] E.K. Uarburton, J.W. Olness, and A.R. Poletti;

Phys. Rev. 160_ (1967) 938.

[15] P. Paul, J.B. Thomas, and S.S. Hanna;

Phys. Rev. 147_ (1966) 774.

[16] L.G. Elliot, and R.E. Bell;

Phys. Rev. 76_ (1949) 168.

[l7] D.St.P. Bunbury, S. Devons, G. Manning, T.H. Towle;

Proc. Phys. Soc. (London) A69_ (1956) 165.

[l8] A.L. Catz, and S. Amiel;

Nucl. Phys. A92^ (1967) 222.

[l9J 0. Beckmann, and R. Sandstrom;

Nucl. Phys. 5^ (1958) 595.

[20] C.P. Swann, V.K. Rasmussen, and F.R. Metzger;

Phys. Rev. 114_ (1959) 862.

[2l] W.L. Mouton, J.P.F. Sellschop, and R.J. Keddy;

Phys. Rev. 128_ (1962) 2745.

[22] E.C. Booth, B. Chasan, and K.A. Wright;

Nucl. Phys. 57_ (1964) 403.

[23] T. Lauritsen, and F. Ajzenberg-Selove;

Nucl. Phys. 78_ (1966) 1.

[24] C. van der Leun, and C. Alderliesten;

Nucl. Phys. A380 (1982) 261.

[25] M.L. Stelts, and J.C. Browne;

CHAPTER 3

(Accepted for publication in Z. für Phys.)

INVESTIGATION OF EXCITED STATES OF nB AND 7L i BY MEANS OF THERMAL NEUTRON CAPTURE ON 1 0B NUCLEI

P.J.J. KOK, J.B.M. DE HAAS and K. ABRAHAMS

FOM-ECN Nuclear Structure Group, Energieonderzoek Centrum Nederland, Petten, The Netherlands

H. POSTMA

Lab, voor Technische Natuurkunde, T.H. Delft, Lorentzweg 1, Delft, The Netherlands

and

W.J. HUISKAMP

Kamerlingh Onnes Lab., Rijksuniversiteit Leiden, The Netherlands

ABSTRACT

The Y-radiation from the 1 0B(n,Y) reaction Is studied using an un-polarlzed target. More accurate values for energies of transitions in

B could be determined. No new levels have been found. The Q value of this reaction: 11454.1(2) keV, is in agreement with earlier experi-ments. Also a new value for the cross section could be derived: 0.29(4) barn, which is a factor 5 more accurate than earlier experi-ments.

The 1 0B(n,a)7Li reaction, leading to the 478 keV state in 7H , is studied by means of polarized 1 0B nuclei and polarized neutrons. The resulting anisotropy in the directional distribution of the 7Li parti-cles manifests itself in the Doppler broadening of the 478 keV line. Analysis of the line shape directly yields the conclusion, that the reaction proceeds for more than 96% through the J » 7/2 channel of nB in case of destructive channel interference of the J = 5/2 channel. Constructive channel interference is only possible if the reaction proceeds for more than 99.5% through the J = 7/2 channel. It appeared

that the outcoming a and 'Li particles are emitted predominantly in directions perpendicular to the nuclear orientation axis.

3.1. Introduction

In this paper the 10B(n,ctY)7l,i and 1 0B ( n , Y )nB reactions have been investigated by means of thermal neutron capture using polarized as well as unpolarlzed boron nuclei. The cross section for the (n,a) reac-tion is 3837 b [l], and for the (n,Y) reacreac-tion it is 0.5 b. Therefore, the count rate for the (n,Y) reaction, as described in the first part of this paper, is considerably reduced. Reports on this (n,y) reaction are scarce (see [2]).

A reinvestigation of the 1 0B(n,Y)1 1B reaction with improved techni-ques is expected to yield a better value for the o capture-cross sec-tion. Other information about the decay of excited boron nuclei can be obtained by measuring the recoil broadening of the transitions. In light nuclei (A<20) it is possible to distinguish between primary and secondary transitions (see [3]) by measuring their full-width-half-maximum (FWHM) values. Only the secondary transitions may show Doppler broadening.

The second part of this paper reports about investigations on the 478 keV y-transition in the subsequent 'Li* decay, following the 1"B(n,a)7Li* reaction. The line shape of this transition should give some insight in the wave functions of the capturing state of 1^B. Es-pecially a better knowledge of the contributions of the 7/2+ and 5/2+ capturing state amplitudes is of importance to parity non-conservation experiments [4,5].

The common use of the ^ B ( n , a ) reaction as a standard in neutron physics gives both experiments practical interest, because the under-standing of this reaction requires a detailed knowledge of the ^ B system.

3.2. Investigation of the 1 0B(n,y) reaction with unpolarlzed boron nuclei

3.2.1.^Experimental

Gamma radiation from the excited ^ B nuclei has been detected by a high purity p-type germanium (HPGe) detector with a relative efficiency of 5%. In coincidence with two Nal(Tl) crystals, the detector serves as a pair spectrometer, operating in the energy region between 2 and

11.4 MeV. Because of the large cross section for the competing (n,a) reaction compared to the (n,Y) reaction, only about 1 out of every 8*103 neutrons are available for the latter reaction. Single count rates for the Nal(Tl) crystals, and for the HPGe detector were of the order of 1.3*10'* counts/s, and 3*10' counts/s respectively. Consequent-ly the triple coincidence rate of the pair spectrometer amounts to never more than about 1 count/s. Reasonable statistics for the lower intensity peaks could therefore only be reached in long runs; up to 1300 h of measuring time was used. Boron nitride (BN), containing 42 wt% natural boron, 53 wt% natural nitrogen, 1.5-2.5 wt% boric acid, and among others small amounts of chlorine and carbon were used as tar-get in this experiment. The ll4N(n,Y) reaction provides suitable cali-bration lines for the pair spectrometer [6,7].

The energy region between 0.3 and 3.9 MeV has been covered with the HPGe detector operating during 24 h in single mode. In this measurement a sample of natural boron was used. The spectrum has been calibrated with 3 5Cl(n,^) transitions [8] using an Fe-Cl, crystal as a sample.

By means of a dummy-carbon target, background contributions could be determined. With an 8k ADC, used for both experiments, the data are stored into the memory of a computer, where the spectra are written every 12 h on tape for further handling. Due to the low count rate of the pair spectrometer the stability of the amplifier must be checked carefully. This can be done by looking at closely spaced doublets, and omitting those spectra, where these doublets are more or less unresolv-ed, depending on the amplifier drift. In the analysis the 7.631 MeV and 7.645 MeV Fe background doublet proved to be suitable for this purpose.

3.2.2. Gamma-ray sgectrum analaysis

The single as well as the pair spectra were summed, allowing for minor corrections related to zero-point and gain shifts. Due to charge trapping in the HPGe detector a small asymmetry is present in the line shape. Therefore the lines were fitted with a gaussian function modi-fied with a small asymmetry term. Background lines could be attributed to Sb, Si, Ge, Cr, Co, Cl, Cu, Fe, C, Al, Ti, Ni and Ca.

Knowledge of the intensity ratio of the boron and nitrogen lines of the target is necessary for a calculation of the absorption cross sec-tion o of 1 0B . The determination of this ratio is somewhat troubled by

a contribution to the 1 4N(n,Y) spectrum from y-radiation emitted by N nuclei in air. A measurement with the dummy-carbon target gives an estimate of the amount of neutron capture of N nuclei in air, compared with neutron capture of Si and Fe nuclei in the background. Knowledge of the intensity of several of those background lines is necessary to check for potential influences of the target geometry. From the peak contents of these background lines, but now measured with the natural BN target, it is concluded that 13(1)% of the neutron capture in nitro-gen arises from air.

Because transitions of heavier nuclei (A>20) and the primary transi-tions of the light nuclei, do not show significant Doppler broadening [ 3 ] , they are used to determine the detector resolution. In figure 1 a plot is drawn of the FWHM of the primary and secondary transitions in ^ B , 1 5N , and of some of the stronger background lines. The detector resolution measured at the calibration lines is fitted in a x2 analysis to a second order polynomial. It appears to be almost a straight line between 2 and 11 MeV, as can be seen in the figure. In table 1 the FWHMs of the secondary transitions are compared with the expected de-tector resolution taken from figure 1 at the same energies. See for a further discussion section 3.2.4.

3.2.3. Level scheme and cross section of the 1 0B(n,y) reaction The analysis of the single spectrum revealed only two 1 0B(n,Y) tran-sitions (2296 kéV and 2533 k e V ) , that have also been seen in the spectrum taken with the pair spectrometer. However these transitions can be determined more accurately from the pair spectrum. Therefore the energies and intensities of the measured Y-transitions are only

calibrated with the lf*N(n,Y) lines, and are compared in table 2 with the values given by Thomas et al. [2J. The agreement is excellent, leading to the same decay scheme with improved energy determination (see figure 2 ) . A further search for other transitions, possible in this scheme, and for transitions to levels known from other reactions (see [9]) gave negative results. Hence we conclude, that intensities of such lines are below about 5% of the total capture intensity. This is in agreement with the empirical rule, that primary transitions of dipole nature are dominant; primaries of other multipolarities are expected to be very weak.

keU

4\

tt

7

6

5

4

3

2

-ï

,1

5

ï

T^T "

-L

10

12

Flg.1. The experimental line widths of (n,-y) transitions.

A background transltl ons and

primary transitions In tl and

B

X secondary transitions ln

B

O secondary transitions in tt

The solid line Is a fitted curve to the primary

trans 11Ions.

TABLE 1

The FWHM of secondary (n,Y) transitions In ' ' B and 1 5N nuclei, compared to the detector resolution

energy (keV) 4444.03 5269.07 5297.66 6322.25 6738.34 8309.81 8916.80 9148.62 exp. FWHM* (keV) 6.11(22) 4.24(10) 4.86(14) 6.09(19) 6.59(34) 5.36(30) 6.49(23) 6.81(73) detector resolution (from fitted curve)

(keV) 3.82 4.19 4.20 4.67 4.87 5.60 5.89 6.00 theor. FWHM** (keV) 6.32 6.81 6.56

* The recoil broadening of some of the 1 5N transitions is less than would be expected. The reason for this is that the levels concerned are not only fed by primary transitions, but also by secondaries. ** Calculated here is the Doppler broadening caused by isotropic

dis-tribution of the recoil vectors. If the YY_correlation is taken into account, the values are only slightly different. Therefore the re-sults of these calculations have been omitted.

1 1 4 5 4 . 0 8 ( 1 9 ) 1 1

4 . 5 ( 0 . 3 ) 5 5 ( 2 )

8 9 2 0 . 4 4 ( 2 7 )

5 7 4 1 . 7 6 ( 2 4 )

4 4 4 4 . 9 5 ( 1 5 )

—I 1 ( 5 / 2 , 7 / 2 )

1 2 ( 4 ) 2 8 ( 2 )

5 / 2

-1 3 ( -1 )

-¥-

I

SL 2 .

-¥-

- 7 / 2 "

1 9 ( 2 )

- 5 / 2 "

1 1 4 5 3 . 7 4

°

-

2 2 9 5 . 8 7

-

4 7 1 2 . 2 5

- 3 / 2 "

4 4 4 4 . 9 9

8 9 2 0 . 6 8

B

TABLE 2

Energies and intensities of °B(n,Y) gamma rays as measured with the pair spectrometer

E

Y

(keV)

2296.61(59)

2533.49(23)

4444.03(12)

4711.17(10)

6738.34(50)

7006.75(10)

8916.80(27)

11447.35(52)

I

(%)

7(4)

12(4)

67(4)

28(2)

19(2)

56(2)

13(1)

4 . 6 ( 0 . 3 )

E

r

(keV)

0.26

0.31

0.96

1.08

2.21

2.40

3.88

6.39

E + E

Y r

(keV)

2296.87(59)

2533.80(23)

4444.99(12)

4712.25(12)

6740.56(50)

7009.15(19)

8920.68(27)

11453.74(52)

E + E *

Y r

(keV)

2295(2)

2534(2)

4445(2)

4712(2)

6741(2)

7008(2)

8920(2)

11453(2)

I*

(%)

10(3)

15(2)

65(3)

25(1)

19(1)

54(3)

15(2)

6(1)

to be Q = 11454.1(2) keV, where the error consists of 190 eV statisti-cal part and a 31 eV systematistatisti-cal part [ö], and is therefore mainly statistical. Results are in good agreement with, but more accurate than, the earlier values of 11455(1) keV (Rasmussen et al. [lOj, and 11453(2) keV (Thomas et al. [2J). Errors in these values are also presumed to be mainly statistical.

The large cross section of the competing (n,a) reaction makes a de-termination of the (n,Y) cross section troublesome, therefore the ex-isting value for the cross section a = 0.5(2) b [l] is difficult to improve. However, the gamma-ray spectrum measured with the natural BN sample gives a good opportunity to calculate the cross section of boron more precisely by comparison with the cross section value of ll4N(n,Y) reaction [ l ] , which is 75 ± 7.5 mbarn. In order to reduce systematic errors due to influence of the efficiency of the pair spectrometer, two distinct and closely spaced lines of B and N have been chosen for the calculation; that is; the 4444 keV 1 0B(n,Y) transition of intensity 65(3)% [2] with peak area of 4950(118) counts is compared with the 4509 keV 11(N(n,Y) transition with intensity of 16.6(3)% [7] and peak area of 1868(69) counts. For these two lines the efficiency of the pair spectrometer differs less than 1%. After correction for the 13(1)% background in the (n,Y) spectrum due to nitrogen in air, the background contribution of boron is negligible, a new cross section value of 1"B is obtained, that is:

a = 0.29 ± 0.04 barn (quadratically compounded errors),

which is a factor of 5 more accurate compared to earlier measurements

UI-3.2.4. Line shape of primary and secondary y-transitions

A further confirmation of the level scheme can be found in the obser-vation of the line widths of the (n,y) transitions. Primary transitions will always show slight shifts to lower energies in comparison to the transition energy; the primary transitions will, however, not be broad-ened. In the case of secondary transitions this will be different. In addition to their own recoil energy reduction there will be Doppler broadening of the lines, due to the recoil of the nucleus by the

pre-ceding (primary) transitions, which have given the nucleus a velocity in largely random directions (neglecting the effect due to directional correlations between y-rays in cascade).

To determine the line shape of secondary transitions, one must know the intensity as a function of the Doppler shift. If there is no direc-tional correlation between primary and secondary gammas, and v is sin-gle valued, a simple relation can be derived between intensity 1(9) and energy shift AE. The intensity I(9)d9 in a direction between 9 and 9+d9 is proportional to the probability P(9) of finding a recoil vector v in that direction. In general the following equations holds:

2ir

P(AE) = ƒ P(9,4>)d<jl sin9 [d(AE)/d9] (1) o

for the probability as a function of the Doppler shift, where P(AE)d(AE) = P(9,cj>)sin 8 d8d$ and the angles 9 and $ are defined in figure 4. This equation simplifies in the case of an isotropic distri-bution of recoil vectors, v, i.e. P(9,<t>) = 1/4TT, to

P(AE) = (2v/c E )- 1. Neglecting the influence of the stopping power, it is clear that with a perfect detector resolution the line shape is rectangular (see also [l9J). For comparison with experiment, this rectangle must be convoluted with the detector resolution. In figure 1 and in table 1 the broadening of the dominant gamma peaks with respect to the detector resolution is clearly visible for several secondary transitions. In the last column of table 1 we give calculated line widths of three secondary transitions in the 1 0B(n,Y) reaction using

the above-given model and convoluting with the detector resolution. As the lifetimes of the levels concerned are shorter than 15 fs [24], it is expected that the lines will show maximum Doppler broadening. The stopping power of the surrounding medium cannot noticeably diminish this broadening in such a short time. Calculations have also been made of the Influence on the line shape of the angular distribution of the recoil vectors, as a consequence of correlations between primary and secondary Y-transitions. In table 1 the results are shown only for the isotropic distribution, because the values are within experimental error the same as for the anlsotroplc case. These considerations agree with experimental values as has been given in the table and with [3].

3.3. The 1 0B(n,a) reaction investigated with polarized boron nuclei

3.3^1 ^Introduction

Thermal neutron capture by 1 0B nuclei will lead, under emission of an a-particle, in about 93% [lo] to the 478 keV excited state of 7Li (see figure 3 ) . The reaction energy will be shared on. basis of momentum and energy conservation by the a and 7H particles. As a consequence the recoiling 7Li particle will get a kinetic energy of 0.84 MeV. Hence the 478 keV gamma ray will be Doppler broadened. From section 3.2.4. the maximum Doppler shift of this transition is calculated to be 7.6 keV. As the 478 keV level has spin I = 1/2, the Y-radiation will be emitted isotropically in the center of mass system with respect to the 7Li spin direction. Therefore, in the case of unpolarized boron nuclei, and neglecting detector resolution, the line shape will be rectangular with a maximum broadening of 15.2 keV. According to the finite lifetime of about 102 fs [25], the excited 7L i nuclei may collide with surrounding matter before the emission of the 478 keV photon has taken place, losing thus part or all of their energy. Instead of one rectangular line shape, the 478 keV peak can be thought to consist of a histogram summation of several rectangles. For each of these rectangles its width will depend on the velocity of the 7L i nuclei, and its height on the lifetime of the level, by means of the exponential decay law, as has been demonstrated by Neuwirth et al. [19].

If, in addition, the boron nuclei are oriented, an anisotropy in the emission of the a-partides will result, concomitantly with an aniso-tropic angular distribution of the recoiling 7Li nuclei. With the Ge(Li) detectors we measure, however, not the angular distribution of the a or 7Li particles, but that of the gammas emitted by the excited 7Li* nuclei. Because these gammas are emitted isotropically in the center of mass of the 7L i * nuclei, the difference in intensity of ir-radiation from parallel and anti-parallel polarized neutron capture by a polarized target, must be the same for detectors placed in different directions with respect to the nuclear orientation axis. The anisotropy will therefore be confined to the Doppler broadening of the 478 keV transition and will result in a different line shape.

As a consequence the capture channel spin mixing coefficient a

( S / 2 , 7 / 2 )

3 / 2 "

Flg.3. The

B<n,w'>

LI reaction.

Also the direct trans i 11 on to the ground state of the

(n,Y> reaction has been plotted. Even L-values for the

ex -emission are forbidden due to the parity change.

Other odd L—values are excluded on the basis of vector

add 11Ion requirements.

with polarized neutrons through a polarized nuclear target (see e.g. Ferguson [ll] or Bosman and Postma [l2]). First, by measuring the rela-tive difference between parallel and anti-parallel counting rates, and secondly, by fitting the line shape of the 478 keV transition with theoretically calculated line shapes. The second method has the advan-tage, that it contains as a proportionality factor the product of the polarizations of target and neutron beam, which are often difficult to measure precisely, but do not basically Influence the fitting procedure of the line shape.

2i2:.2^jnie_targ^t_£olarization

Investigation of the anisotropy In the 'Li distribution requires polarization of the 1 0B nuclei. This has been achieved by the so-called "brute force" method, in which only an external magnetic field acts on the nuclei. A polarizing field of 7.5 Tesla has been used. The very low temperatures needed were obtained with a PrNi5 cooling stage attached to a dilution refrigerator. (For further details see Tielens [20].) Even with a heavy target (3.8 g) it was possible to reach a sample temperature of order 15 mK and retain it during long periods.

As a target, enriched boron (90% 1 0B , 10% UB ) alloyed with pure aluminum has been employed. For the target preparation 0.4 wt% of en-riched boron was molten together with 99.9% pure aluminum by means of a levitation melt in a high frequency furnace. The final result is a target of disk-like shape with diameter 2.51 cm and 0.15 cm thick. For a good thermal contact, this sample was electron-beam welded to its aluminum holder. The boron experiment was combined with measurements on "•^Ti [l4J. A titanium target has therefore been mounted against the A1(B) target.

The target was irradiated with a 0.088 eV neutron beam, which was polarized by means of Bragg reflection from a magnetized C^MnAl Heusler single crystal. By means of a fission counter, placed behind the sample, the total neutron flux through the target was monitored. A second analyzing Heusler crystal and a BF, counter, both also placed behind the target, were used to determine the mean neutron polarization at the place of the sample; it was deduced to be f = 71(3)%. With an r.f. splnfUpper device the direction of the neutron spin could be reversed periodically. In that way It was possible to do experiments

with parallel and anti-parallel switching of the directions of neutron and target spin.

The sample temperature could be monitored with the aid of a 6 0C o nuclear orientation thermometer, consisting of a needle-shaped cobalt single crystal. This 6 0C o thermometer was mounted onto the bottom of the target, and due to bad heat contacts was mainly be used to indicate whether the sample was in the 5-20 mK region.

For titanium the temperature could be determined accurately from observing the 6058 keV "*9Ti(n,Y) primary transition [l4], which pro-ceeds through the J = 4 channel entirely (J = I + 3/2). From the theo-retically known y-anisotropy the temperature of the Ti nuclei could be derived. In principle this method could also be used to determine the temperature of the Al nuclei [15], but the measurement of the radiation anisotropy in the aluminum transition is troubled by a large amount (about 85%) of background radiation from aluminum in the refrigerator. However, it can be suitably used as a monitor for temperature varia-tions.

Anisotropy effects in 2 8A 1 ^-transitions as well as transmission effects of the boron 478 keV line, with the target in the millikelvln region show a temperature lag between the cooler aluminum nuclei and the "hotter" boron nuclei. From observing the difference between the parallel and anti-parallel spectra, we found a steady cooling rate of the 1 0B nuclei of 1.5*10~7 K/s, that is from 100 mK to 50 mK in four days. The slow cooling rate can be explained by a high Korrlnga con-stant ( K = 3*10"* Ks [l3]), which governs thé nuclear spin-lattice re-laxation. When the effect in the spectra of the 478 keV transition has been stabilized, the temperature is assumed to be the same for titanium and boron nuclei. From the effect in the 6058 keV 't9Ti (n,Y) transition the temperature could then be calculated, which was 15(3) mK. At that time a polarization had been reached of 15(3)% for the 1 0B nuclei. This agrees fairly well with the temperature determined from the 6 0C o ther-mometer, which was 10(1) mK according to [14] during the period in which our measurement was performed.

Spectra in 2560 channels in the energy region between 250 keV and 640 keV were recorded every half hour simultaneously with two Ge(Li) detectors in the directions 6 = 0 ° and 8 = 90° with respect to the polarizing magnetic field (see also figure 4 ) . The first 1280 channels of each spectrum contain information about the sum of parallel and

rn I x I ng chamber

heat suItch £ 3 [

demagnetization field

C7.5T)

horIzontal

detector

(0 = 90° >

neutron beam

polarization field

(GT)

vertical detector

(0

=

0°)

X

Fig.4. ft schematic representation of the nuclear orientation

set up uilth belou a nomenclature of the used direct I ons.

anti-parallel capture, and the second 1280 channels about their

differ-ence. Both detectors have a relative efficiency of 15% and the FWHM at

1.33 MeV is 2.6 keV and 2.7 keV for the vertical and horizontal

detec-tor respectively. Data of the beam monidetec-tors together with the results

of the spectra were stored and dumped on tape once in every 12 hours.

3.3.3. The directional_distribution of the a and

Li particles

For an extensive treatment the reader is referred to [11,12,21]. Only

a short review will be given here. In general the directional

distribu-tion of radiadistribu-tion can be represented by an expansion in Legendre

poly-nomials [ 16 ]:

k k

W(9) =

I K

\ (n)f (I)P (cos6), (2)

k k

k

\

2

k

l

2

where A^ are coefficients of the directional correlation function,

depending on initial, intermediate, and final spins of the transitions.

Further they depend on the angular moments of the emitted radiation, L,

and in the case of mixed transitions on the interference between them.

For a-emission the A-coefficients can be expressed in those of

Y-radia-tion using the well-known particle parameters; that is:

k k k k

A

(a) = A

( y ) b

(3)

The parameters f (n) and f ( I ) r e p r e s e n t t h e o r i e n t a t i o n of t h e n e u

-\

2

trons and of the nuclei respectively; always f = 1 , and for

convenien-o

ce we will call the neutron polarization f,(n) in the text f and the

1 n

target polarization f (I) will be called f . The summation indices are

restricted to: 0<k <1; 0<k.<21; Ik -k |<k<k -He ; furthermore, k and

k+k -He must be even.

In our experiment

B nuclei (u = 1.80

\i ) were oriented in an

exter-N

nal magnetic f i e l d of 7 . 5 Tesla a t a t e m p e r a t u r e of 15 mK. Consequently

only t h e p o l a r i z a t i o n parameter f i s i m p o r t a n t ; n u c l e a r o r i e n t a t i o n

p a r a m e t e r s with index k >1 a r e n e g l i g i b l e . This leads t o the s i m p l i f i e d

e x p r e s s i o n :