(3He, 2n) excitation functions for some light nuclei

1 LA.1 1

Nuclear Physics A235 (1974) 11-18; Not to

@ North-~o~~aad Pab~ish~ng Co., A~sterdu~

be reproduced by photoprint or microfilm without written permission from the publisher

(3He, 2s) EXCITATION FUNCTIONS FOR SOME LIGHT NUCLEI t C. E. MOSStt and C. S. ZAIDINS Nuclear Physics Laboratory, Department of Pkysics and Astrophysics, Umiversity of Coforado, Boulder, Colorado 80302 USA Received 26 August 1974 Abstract: Excitation functions have been measured for the reaction gBe(3He, 2n)l°C over the range E(3He) = lo-41 MeV and for the reaction 27Al(3He, 2#*P over the range E(3He) = 14.41 MeV by detecting &delayed y-rays. An excitation function has also been measured for the reaction 24Mg(3He, 2r1)~~S.i over the range E(3He) = 21-43 MeV by detecting B-delayed protons.

E

NUCLEAR REACTIONS 9Be(3He, 2n), E = lo-41 MeV; 24Mg(3He, 2n), E = 21-43 MeV; 27Al(3He, 2n), E = 14-41 MeV; measured b(E3&. Natural and enriched targets.

1. Introduction

There have been many measurements of (3He, xn) cross sections on nuclei with A > 50, but we are aware of only two measurements on targets with A 5 50. These are cross section measurements for the reactions 37C1(3He, 2n)38K [ref. ‘)I and ’ 60(3He, 2n)l 7Ne [ref. ‘)I. The (3He, xn) reactions can lead to very proton-rich nuclei which are of considerable interest 3*‘). For example, the reaction 28Si(3He, 2n)“S yields a product nucleus whose existence is known “) but for which a detailed study of the ~-transitions to both bound and unbound levels in 2gP has never been reported. The reaction 28Si(3He, 3n)% yields a product nucleus whose existence has never been reported. It is desirable to have good estimates of the cross sections for the (3He, xn) reactions in order to design experiments to study proton-rich nuclei such as these via (3He, xn) reactions. In heavy nuclei the statistical model gives fairly good predictions for (charged particle, xn) cross sections “). In light nuclei the statistical model predictions are not expected to be as good because multiple neutron emission is a much smaller part of the total reaction cross section. In the present study we have measured the cross sections as a function of the bombarding energy for the reactions 9Be(3He, 2n)l°C!, 24Mg(3He, 2n)‘%i, and 27Al(3He, 2n)28P. A preliminary report of this work has been given ‘). These measurements together with the two measurements mentioned above provide a small data set on which to base estimates of other (3He, xn) cross sections for light nuclei. r Work supported in part by the US Atomic Energy Commission. rt Present address: Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87544. II

12

c. E.

MOSS AND C. S. ZAIDINS

2. Experimental procedure

The cross sections for the reactions 9BeeHe, 2n y °c and 27 AleHe, 2n Y8 p were determined by observing fJ-delayed y-rays. The experimental set-up is similar to that used in several previous studies [for example, see ref. 8)] and is described in detail in ref. 9). Beams of 3He+ + particles from the University of Colorado variable energy cyclotron were limited to 12-70 nA for the Be target and to 350-440 nA for the Al target in order to keep the Nuclear Data 50/50 analyzer dead time below 25 %. The beam emerged from the vacuum system through a 0.00254 cm thick Havar window (21 mg/cm 2). The Be target contained 99.8 % Be and was 0.0025 ± 0.0003 em thick. It was necessary to sandwich the Be foil between two Al foils each 0.0018 cm thick because the Be foil was too brittle to withstand the mechanical shocks of the pneumatic shuttle. The Al target contained 99.999 % Al and was 0.0051 ±0.0005 cm thick. Appropriate energy loss corrections 10) were made to determine the energy halfway through the target. The targets were transferred by a pneumatic shuttle with a transit time of about 0.3 sec between the cyclotron vault target chamber where they were irradiated and a low-background counting area 5 m away. There a 34 cm 3 Ge(Li) detector was used to collect four successive y-ray energy spectra. Lucite 2.54 cm thick was placed between the target and the detector for the Be measurements; lucite 5.08 cm thick and lead 2.54 cm thick were used for the Al measurements. The length of the sequential time bins for each spectrum was 16 s for the Be target and 0.2 s for the Al target. The total measurement time for each energy point ranged from 2 h to 4 h for Be and from 4 h to 14 h for AI. The efficiencies of the Ge(Li) detector in the geometries used in this experiment were determined with a 56CO source and a set of standard sources for which the absolute intensities were accurately known. Because it was difficult to accurately measure the beam current with these semithick targets in front of the Faraday cup, a new time period was added to the sequencer controlling the pneumatic shuttle. With the target at the counting position, the charge incident on a Faraday cup at the irradiating position was measured for a known period of time. The ratio of the length of time during which the target was actually irradiated to the length of time of this "dummy irradiation" multiplied by the dummy charge is an accurate measure of the charge striking the target when averaged over many cycles. The cross section for the reaction 24MgeHe, 2n) 25 Si was determined by observing fJ-delayed protons with a silicon surface barrier detector in a large scattering chamber. Beams ranged from 80 to 500 nA. The target contained > 99 % 24Mg and was 0.72±0.07 mg/cm 2 thick based on a-gauge measurements. Instead of moving the target, the pneumatic shuttle sequencer was used to operate a pneumatic piston which pulled the detector back 2.3 cm during irradiation to reduce radiation damage. During the counting period, four successive proton energy spectra were collected with the detector 1.35 cm from the target. The time bin for each spectrum was 0.2 s, and the total measurement time for each energy point ranged from 2 h to 19 h. From the

f3He, 24

13

geometry defined by the collimator in front of the detector, it was calculated that (0.9 kO.1) % of the protons emitted by the target were detected.

3. Analysis of data The following formula was used to calculate absolute cross sections:

where

and rr = absolute cross section in barns; Z = charge of the ions in the beam in units of the charge of the electron; I. = decay constant in s-l; Tt = irradiation time per cycle in s; C,, = total number of counts in the first time bin for all cycles after correction for dead time; Q = total irradiation charge for all cycles in PC; p = target thickness in atoms/cm2; E = efficiency for detecting disintegration (this includes both the detector efficiency as well as any applicable branching ratios); TG = total cycle time in s; Z$ = transit time in s allowed for target transfer from the irradiate position to the counting position; LIT = time per time bin in s. Note that lim

E;(I, N, T,) = I.

N1T,+m

The quantity Co was determined by fitting a straight line to the logarithms of the peak areas in the four spectra. The half-lives used for the radioactive nuclei 1‘C, *‘Si, and 2sP were 19.41 kO.04 s [ref. ‘“>I, 21X&4 ms [ref. ‘“)I, and X3&4 ms [ref. 13)], respectively. For “C, 100 % of the decays yield a 717 keV y-ray I’), and this y-ray was used to determine the gBe(3He, 2n)l’C cross section. For 28P, 11 % of the decays yield a 4498 keV y-ray 14), and the full energy, single and double escape peaks were used to determine the 2 7Al(3He, 2n)28P cross section. An accurate experimental absolute P-branching ratio for 2 ‘Si has not been reported and therefore the branching ratio must be cafculated. The calculation is based on well-established p-decay theory and should be quite accurate. The proton group observed was the 4.26 MeV group [see fig. 2 and refs. I29t 5)] which results from the superallowed P-decay to the 7.92 MeV, T = 3 level in 2‘Al followed by proton breakup to the 1.37 MeV level in 24Mg. Wilkinson and Alburger calculate that for the superallowed decay to the 7.92 MeV level in 2SAl, ft= 1944&90 [ref. ‘“)I. Using 3.824+0.010 MeV for the mass excess of z5Si [ref. “)I, -8.912+0.001 MeV for the mass excess of 25AI [ref. “)], and 7.916+0.006 MeV for the excitation of the analog in 25Al [ref. ‘“)I, we calculate that the rn~irn~ pi energy is 3.798-&0.012 MeV. Combining this with the known half-life 0.218 50.004 s leads to f = 1003 + 14. Thus

Be8 Al + 26 MeV 3He

IOIIIIIIiIIIIIIIIlIIIIIIIIIllIIIIlIIlIIIIIIIIIIIIIIIIIIIIIIIIIlIIIIIIIIlllllliil~lilllllill 200 400 600 Channel

600

1000

Fig. 1. A p-delayed y-ray spectrum obtained in the first time bin for 26 MeV 3He incident on a Be target sandwiched between Al foils. The peaks are labeled with the parent nucleus and the y-ray energy 5*11*24--26). One or two primes denote single or double escape peaks, respectively. The 717 keV y-ray was used to determine the gBe(3He, 2n)l°C cross section. 5O~l,,,,,,,,,,,,,,,,,

I I,,,,,,,,

I ,,,,,,,,,,,,,,,,I,,,,/,,,,,,

24Mg+41

I,,1 I,,,,,,,,,,

MeV 3He

800

1

Ioc10

Channel

Fig. 2. A p-delayed proton spectrum obtained in the first time bin for 41 MeV 3He incident on a 24Mg target. The peaks are labeled with the proton energies in the center of mass 5r12*15). The 4262 keV peak was used to determine the 24Mg(3He, 2n)*%i cross section.

15

(3He, 2n)

Channel Fig. 3. A &delayed y-ray spectrum obtained in the first time bin for 21 MeV 3He incident on a 27A1 target. The energies shown are taken from the literature 5,14*26). The 4498 keV y-ray was used to determine the 57A1(3He, 2n)2*P cross section. See caption to fig. 1.

600

,

,

,

,

I

I

,

I

I

I

I

,

,

gBe(3He,2n)‘oC

1ii

5OO-

400C _n .5300b

I

i

200”.’

If

:

I

100 11 0

’ 6

’ IO

’

I 14

’

1 18

’

’ 22

’

’ 26

’

’ 30

’ 34

E&MeV) Fig. 4. Experimental are reIative statistical

excitation function for the reaction gBe(3He, 2n)l”C. The error bars shown errors. There is an additional error of 14 % in the absolute normalization. The threshold for this reaction is E(3He) - 7.39 MeV.

C. E. MOSS AND C. S. ZAIDINS

0

18

22

26

E,$fl&)

34

38

42

Fig. 5. Experimental excitation function for the reaction 24Mg(3He, 2r~)~~Si. The error bars shown are relative statistical errors. There is an additional error of 33 % in the absolute normalization. The thresholdfor this reaction is E(JHef = 21.34 MeV.

1000 900

800

700

= 3

600

b 500 400 300 200 too 0

10

14

18

30

34

38

Fig. 6. Experimentat excitation function for the reaction 27Al(3Be, &Q*P. The error bars shown are relative statistical errors. There is an additional error of 14 % in the absolute normalization. The threshold for this reaction is E(3He) = 1 X.91 MeV.

the partial half-life for the p-decay to the analog is 1.938 + 0.094 s, or the P-branching ratio is (11.2 of:0.6) %. The branching ratio for the proton break-up of the 7.92 MeV state to the 1.37 MeV state in “Mg is X3 % [ref. “)I. If we assume an error of & 5 % on this branching ratio, then the product of the beta branc~ng ratio and the proton

t3He, 2x1)

17

branching ratio is (9.3 kO.7) %. This is the branching ratio which must be combined with the detector efficiency in eq. (1) for 25Si. Since thin targets were used, it was possible for some of the nuclei to recoil out of the target. Corrections for this effect were cakulated by integrating the pure phase space density p of eq. (28) in ref. “) over the target thickness, angle of recoil, and recoil energy. Range data were taken from ref. 21), For the Be target, the Al foils stopped most of the recoils and the effect was negligible (< 1 “/o). For the Al target, a negligible fraction (< 2 “/o) of the recoils escaped because the target was relatively thick. For the relatively thin Mg target, a large fraction of the recoils (80-92 Fd/o> escaped and appropriate corrections have been made. 4. Results

Figs. 1-3 show spectra obtained in the first time bin for the three targets 9Be, ‘“Mg and 27A1. Figs. 4-6 show the cross sections. The errors plotted are relative statistical errors. For energies at which there were several measurements, the values plotted are averages weighted by the squares of the errors. An error estimate of 10 % in the target thickness and an error of 10 % in the efficiency of the Ge(Li) detector lead to an error of 14 % in the absolute cross section for the reactions ‘B@He, 2n)lOC and 27A1(3He, 2n)Z8P in addition to the relative errors shown in iigs. 4 and 5. An error of 10 y0 in the target thickness, an error of 11 *Ain the efficiency of the proton detector, and an error of 30 y0 in the recoil correction lead to an error of 33 y0 in the absolute cross section for the reaction Z4Mg(3He, 2n) 2sSi in addition to the relative errors shown in fig. 6. 5. Diseussioa Attempts were made to fit the excitation functions with the code ALICE 22) which is based on the statistical model. This code has been very successful for A > 50, but for the present excitation functions the predicted cross sections were more than an order of magnitude too small. However, the shapes roughly agreed with the data. An attempt to fit the 37C1(3He, 2n)38K data also gave a predicted cross section that was much too small, butthe predicted cross section for the 56Fe(3He, 2n)5 7Ni reaction was within a factor of 2 of the data 23). With light nuclei much of the total reaction cross section involves the emission of charged particles, and the cross section for the emission of two or more neutrons is very small. It is thus not surprising that large errors can occur in very small parts of the total reaction cross section. More study is needed before the statistical model can be used to make reliable predictions of the cross sections for the emission of two or more neutrons to nuclei with A c 50. We would like to thank Dr. P. D. Ingalls for assistance in collecting the data and Mr. M. I. Forsyth for assistance in both collecting and analyzing the data. We would also like to thank M. Bfann and C. Fulmer for supply~g us with statistical model programs and helpful discussions.

18

C. E. MOSS AND C. S. ZAIDINS

References 1) D. M. Lee and 5. S. Markowitz, Lawrence Berkeley Laboratory 2) 3) 4) 5) 6) 7) 8) 9)

10) 11) 12) 13) 14) 1s) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26)

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