Tz = case12 β-delayed proton precursors

Nuclear Physics A371 (1981) 344-363 © North-Holland Publishing Company

Tz = } ß-DELAYED PROTON PRECURSORS (II) . The decays of 6SGe and'3Kr

J. C. HARDY, T. FAESTERMANN t, H. SCHMEING, J. A. MACDONALD t', H. R. ANDREWS, J. S. GEIGER and R. L. GRAHAM Atomic Energ~~ of Canada Limited, Chalk Ricer Nuclear Laboratories, Chalk River, Ontario, C'unada KOJ !JO and K. P. JACKSON tr, Physics Department, University oJ' Toronto, Toronto, Ontario, Canada MSS IA7 Received 9 June 1981 Abstract :The ß-delayed proton decays of 6s Ge (tz = 30.8±1 .0 s) and' 3 Kr (t,~ z = 28 .4±0.7 s) have been studied in detail, proton spectra as well as p- y and p-X coincidences being obtained . The fraction of ~sGe ß-decays populating proton-emitting states in 6 'Ga is measured to be (1 .3±0 .5) x 10 -°, and the proton branch in the decay of 'SKr that populates the first excited state in'zSe is (18±4)~ of the total proton decay. Average y-widths at 5.5 MeV excitation have been established to be 200 t 60 meV in 65 Ga and 320f60 meV in "Br. Values for Qec - Bp are measured to be 2300 t 100 keV for °'Ge decay and 3700± 150 keV for "Kr. The data for both decays have been subjected to statistical model analysis with considerable suceess. The back-shifted Fermi gas model gives better results for level densities than the Gilbert and Cameron formulas, although important numerical results extracted from the data are shown to be independent of the details of analysis . No evidence is found for local structure in the ß-decay strength function . A J* assignment of ~* (or possibly ~+) for' 3 Kr gives best agreement with the data.

E

RADIOACTIVITY 63Ge [from `°Ca(zeSi, 2pn)], "Kr [from 6 °Nî(' 60, 3n)] ; measured ß-delayed protons, Eo , IP, T,~z , py-, and yX-, and yX-ray coin ; deduced branching ratios, 6sGa »Br deduced level T z , level densities, ß-strength function . Natural and enriched targets. Ge(Li), Ge, Nal(Tl), surface barrier Si detectors .

1. Introduction Six ß-delayed proton precursors with A = 4n+ 1 and T= _ +~ have so far been pOS1tlVely identified 1-4) : gZC7e33, 34Se 35+ 36Kr37+ 38Sr39+ 40Zr41+ and 48Cd49. Such series, comprising precursors that differ from one another by the successive f NRC Postdoctoral Fellow . Present address: Technical University of Munich, D8046, Garching, West Germany. ft NRC Postdoctoral Fellow. Present address: TRIUMF, Vancouver, BC . t+r Supported by a grant from NRC Canada. Present address : TRIUMF, Vancouver, BC. 349 Da:mba ~98~

350

J. C. Hardy el ul . ; T~

= T ß-deluti~ed proton precursors

addition of two neutrons and two protons, have proved particularly fruitful in the study of light nuclei S .6). Within a series, the similarity among members makes the analysis of experimental data on the one hand more demanding, since a consistent approach must be achieved, while on the other hand it can be more revealing of variations in nuclear structure. The T = ~ series, though still incomplete, is especially promising in this respect since it is the only one known in heavier nuclei, where statistical effects predominate, and it spans a region of dramatically changing nuclear shapes, from nearly spherical at 6s Ge, through strong deformation near A = 80, and back to spherical again at 9'Cd, which is near the closed shell at'°°Sn. Because of their usefulness in testing statistical analysis techniques, considerable attention has already been paid to the study of T: _ ~ precursors. The first paper in the present series') was devoted to the decay of 69Se, and outlined the general methods used for analysis. In addition, average lifetimes have been measured by the proton-X-ray coincidence technique (PXCf) for proton-emitting states in the decay of 69 Se [ref. 8)] and' 3 Kr [refs. 9 . ' °)] . All data on these and other members of the series have been subjected, in a preliminary way 3 ), to a global analysis, the results being sufficiently successful to motivate a more detailed approach along similar lines. We report here the upshot for 65Ge and '3Kr. Beta-delayed y-rays from the decay of 65Ge are known in detail''), and a decay scheme incorporating at least eight y-emitting states in 63Ga has been established. The known spins of these states " .' a), together with the measured logft values for the ß-transitions populating them, determines the ground state JR of 65Ge to be ~- . Information on the ß-decay of '3Kr is rather more fragmentary : although transitions to six excited states in'3 Br are assigned, none of these states has known spin, so the J~ of '3 Kr has not been determined ' 3). Nevertheless, the lifetimes of both precursors are well known and can be used to identify the origin of observed protons - particularly since few neighbouring nuclei are even candidates as delayed proton precursors . For the purposes of the present study there was thus no reason to study ß-delayed y-rays, as we did ') for 69Se, and we devoted our attention entirely to delayed protons. 2. Experimental proced~e Our experimental techniques were similar to those described in the first paper of this series'), to which the reader is referred for. details that will be omitted here . Self-supporting targets of thickness ~ 1 .3 mg/cm2 were bombarded for 30 s with heavy-ion beams from the Chalk River upgraded MP tandem . Periodically, the beam was interrupted by magnetic deflection and the target pneumatically driven in z 2 s from the irradiation position to a counting position 25 cm below, where detectors were arranged to observe it in extremely close geometry . Following the counting period, typically ~ 90 s, the target was returned to its original position

J. C. Hardy et al.

l T ~ ~ ß-delaved proton precursors

35 1

and the cycle repeated. The reactions employed here were a°Ca(zBSi, 2pn) 6sGe at 90 MeV and e°Ni(t6 0, 3n)'3Kr at 75 MeV. Natural calcium (97 ~ a°Ca) and isotopic nickel (enriched to 99 .8 ~ e°Ni) targets were used . Protons were detected in a surface-barrier counter telescope comprised of a 50 mmz x 11 pm thick dE transmission counter and a 300 mmz x 300 ~m thick E-counter . A 200 mmz intrinsic Ge X-ray detector was mounted facing the back of the target behind a 2 .5 mm thick lie absorber, which reduced the number of detected electrons . Gamma-rays were also detected with either an 86 cm3 Ge(Li) or a 7.6 ctn diameter x 7 .6 cm thick NaI(Tl) detector (when higher efficiency was required), which viewed the target through the proton counter telescope . During the counting period, singles events for protons, X-rays and y-rays were routed into eight sequential energy spectra in order to extract lifetime information. Coincidence data for p-X, p-y and X-y were stored, event by event on magnetic tape, for subsequent playback with selected gating conditions. The X-ray and y-ray detectors were calibrated both as to energy and efficiency over a range from 9 keV to 2 .7 MeV with standard sources t of zzNa, saMn, s'Co, e°Co, 88Y, " 3Sn, ' 3'Cs, zosHg and z4t Am ; in addition, lines from 6sGa appeared in the delayed y-spectra, thus providing an internal calibration t t). The proton telescope was calibrated with an z 4r Am a-source, and the linearity of its energy response established by the use of a precision mercury pulser. 3. Experlmentsl results 3 .1 .

65 Ge

DECAY

The energy spectrum of ß-delayed protons observed following the decay of 6sGe is shown in fig. 1 . Our time-sequential proton spectra yield a half-life of 30.8 ± 1 .0 s ; this agrees well with the previously known half-life, 30 .9±0.6 s, which is the average of two y-ray measurements' t). The X-rays measured in coincidence with delayed protons arise from the filling of electron vacancies that were created by electron capture from the precursor. In this region of nuclear masses, the life-times of proton-emitting states are comparable to that of K-shell vacancies, although predominantly the X-rays are emitted before the protons. Thus, most of the X-rays emitted have an energy spectrum characteristic of the proton emitter (i.e. the ß-decay daughter of the precursor), with ~ 20 % corresponding to the next lighter element (i.e. the proton-decay daughter). The coincident X-rays appearing as the histogram in fig. 2a are mostly from gallium, with a possible weak contribution from zinc, and further confirm the origin of the proton activity as an isotope of germanium. The relative intensity of these two X-ray groups (gallium and zinc), which provides r Supplied and calibrated by Le Bureau National de Metrologie, Gif-sur -Yvette, France .

J. C . Hardy et al. / T, = i ß-delayed proton precursors

352

150

w

O

W m

Z

3% 19 % 36 % 4% 28 %

50

J_f I .0

I 1 .5

PROTON

2.0

ENERGY

2.5

( MeV )

Fig. 1 . Spectrum of protons observed following the decay of °SGe ; the scale has been corrected for energy loss in the target . In the close geometry used, target thickness efFects lead to an experimental energy resolution (FWHM) of z 90 keV. The smooth curve is the result of statistical model calculations " .'z) work ; the J` values described in the text . The decay scheme is derived from this and previous for low-lying states in °3 Ga are known but omitted for clarity .

cn

12

z

lo ô U tL O

8 ~-

w m

6

z

4

b

e 6 4 2

9

10

X-RAY

II

ENERGY

12

( keV )

13

Fig. 2 . (a) Spectrum of X-rays (histogram) observed in coincidence with all protons from the decay of s°Ge . The smooth curve represents X-rays measured simultaneously in coincidence with y-rays ; actually the X-rays were characteristic of zinc and have been shifted in energy to correspond to gallium X-rays. (b) Spectrum of X-rays in coincidence with protons from "Kr ; superimposed is the arsenic X-ray, observed in coincidence with y-rays, and shifted in energy to correspond to bromine. In each spectrum a few counts are observed at the energy of the (Z-2) Ka X-ray. These are random coincidences associated with the strongest peak in the X-ray singles spectrum .

J. C. Hardv et al. / T, _ } ß-delayed proton precursors

353

valuable information on the lifetimes of excited states in 6s Ga, can only be reliably extracted with a knowledge of the detailed peak shape for X-rays of a single element as observed in our detector . This shape can be determined from the spectrum of X-rays observed in coincidence with specific, known y-rays - recorded at the same time as the p-X-ray coincidences . Ideally, gallium X-rays would be preferred for comparison with the histogram of fig. 2a, but sufficient statistics could not be obtained for X-rays in coincidence with ß-delayed y-rays from the decay of 6sGe itself. However y-rays following the decay of 64Ga and 6sGa were copiously present, and the zinc X-rays measured in coincidence with them did provide an excellent "standard" X-ray peak shape. It is this "standard" peak that also appears in fig. 2a, shifted in energy (and in KQto-Kß separation) to correspond to gallium X-rays . From these results we can conclude that the ratio of X-rays from zinc to those from gallium (measured in coincidence with protons) is ~ 0.17. The total ß-branching (BRP) from 6sGe to proton emitting states in 6sGa was determined by comparing the total number of observed protons to the peak intensity of the 62 keV y-ray (emitted from the first excited state of 6sGa). The absolute counting efficiencies of both systems were known, the telescope by measuring its geometry, and the Ge detector by standard source calibration ; an on-line pulser yielded the correction for dead-time losses. The average of two concordant measurements of the proton-to-y-ratio was (4.8± 1 .6) x 10-4. 1'he absolute intensity per 6sGe disintegration is known ") to be 0.27±0.05 for the 62 keV y-ray, so the final result for BRP is (1 .3±0.5) x 10-4 . This is not in serious disagreement with another measurement' ¢), (2.7±0 .8) x 10 -4, of the same quantity . 3 .2 . "Kr

DECAY

The energy spectrum of ß-delayed protons from ' 3Kr appears in fig. 3. In this case, time-sequential proton spectra were recorded on several occasions, yielding a weighted average half-life of 28 .4 f 0.7 s. This value incorporates the data used in our first report ') on '3Kr, and so replaces the value quoted there, with which it is also consistent . Previous half-life measurements have relied on ß-delayed y-rays and have not been notably consistent : 34±4 s [ref.' s )], 25 .9±0.6 s [ref. 16)] and 22 ±4 s [ref. l')] ; their average, 26 ± 1 s, disagrees by slightly more than two standard deviations with the delayed proton result . The X-rays measured in coincidence with protons are shown as the histogram in fig. 2b. The predominance of bromine X-rays confirms krypton as the proton precursor. By comparison with the "standard" peak shape, which is superimposed, the ratio of X-rays from selenium to those from bromine is determined to be ~ 0.18 ; this agrees well with the more precise result, 0.176 f 0.012, established in an experiment 1°) specifically devoted to that measurement. The "standard" peak in fig. 2b was obtained in coincidence with y-rays, and was accumulated concurrently with the X-ray-proton data; it is actually an arsenic X-ray appearing in coincidence

354

J. C. Hardy" et a1 .

/ T = ? ß-delayedproton prerursors

6690 1#~ i~~73 Kr

100

0 .66%

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°> 60 c 0

w

m

40 II% 16 % 17% 4% 7% 45 %

Z

73 ar I

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2.0

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PROTON

I

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3.0

ENERGY

(MeV)

I

4.0

Fig. 3. Spectrum of protons observed following the decay of 'SKr ; conditions are as in fig. I . The dashed and solid curves are statistical model calculations with Gilbert-Cameron and back-shifted Fermigas level densities, respectively . The decay scheme is from this and previous ' 3) work .

51 I keV

860 keV

1

0 w m z I 500

y - RAY ENERGY ( keV ) Fig. 4. Spectrum

of

y-rays observed with the Nal(Tl) detector in coincidence with all delayed protons from the decay of'3 Kr .

J . C. Hmdv et a/ . / T = ~ ß-delayed proton precwsors

35 5

with strong y-rays in the decay of' 3 Se, but it has been shifted in energy to correspond with bromine. The spectrum of y-rays recorded with the NaI(Tl) detector in coincidence with protons is shown in fig. 4. In addition to the annihilation radiation, there is clear evidence for an 860 keV y-ray, which corresponds to the decay of the first excited state in ' 2 Se (see the decay scheme in fig. 3a). The branching ratio for protons populating this state was determined by comparing the number of protons in coincidence with the 860 keV y-ray (NP~) to the total number of protons (N~+Np~), having corrected for the efficiency of the NaI(Tl) detector (and assuming an isotropic distribution). The result, plotted as a function of proton energy, appears in fig. 5 ; the total branching ratio, integrated over the whole proton spectrum is 18±4 [cf. 35±9 ~ quoted in ref. Z)] . The measured ratio of positron emission to electron capture is a strong function of the end-point energy for ß+ transitions, and can be used to determine that energy . The positron-emission intensity is related to the number of coincidences between protons and 511 keV y-rays (NPe), while the total number of protons (Np) reflects the total decay intensity (ß + plus electron capture) . The measured ratio NPß/NP is plotted as a function of proton energy in fig. 6. 4. Analysis 4 .1 . GENERAL FEATURES

The techniques used here for analyzing delayed proton decay are based on the statistical model . They were described in detail in the first paper of this series'), and amended later t °) with respect to the PXCI' lifetime measurements . Briefly, if

Z + 0.4 0

n Z 0.3 w

n

Z O FQ

0 .2

L0

2.0

PROTON ENERGY ( MeV)

3.0

Fig. 5 . Number of protons populating the first 2+ excited state in'=Se ( Np ~ ) relative to the total number of protons emitted, plotted as a function of proton energy for' 3 Kr dewy. The curves are the results of statiatiwl model calculations assuming the ground state spin of'~Kr to be (a) }-, (b) }`, (c) ~+, (d) ~* .

J. C . Hardv et al. l T~ _ ~ ß-delayed proton precursors

356

3 .0 Fz

a Z

1

I .5

2 .0 PROTON ENERGY

2 .5 (MeV)

Fig . 6 . Experimental NPp/NP spectrum compared with a curve calculated from the known positron-toelectron-capture ratio and an excited-state population taken from experiment .

IP(Ep)

is the intensity of protons with energy

EP ,

then

r~J ;,.

~

~rP+ry%EP

where Iß is the intensity of ß-decay from the precursor ( 65 Ge or' 3 Kr) to excited state i in the emitter (65 Ga or' 3Br), rPf is the partial width for proton emission between state i and a final statefin the daughter ( 64 Zn or' Z Se), rP is the total protondecay width of state i, and r; is its y-decay width. Here < ~ denotes the (PorterThomas) statistical mean, and the summation is extended over all pairs of states (i, n between which protons ofenergy EP can be emitted. The algebraic manipulations are described in ref. ') . In evaluating eq. (1), we adopt the "gross theory" of ß-decay e ~' 9 ), using a gaussian strength function and a modified Fermi gas model to calculate the GamowTeller matrix element - and hence, Iß - as a function of transition energy . The average proton-decay width of levels with spin J, at excitation Ex we express in terms of the density of levels with that spin, p.r~(Ex), and the transmission coefficient T;(Ep ) of protons with energy EP and angular momentum 1 t

where the sum includes all values of 1 permitted by the spins and parities of states i andf. As before'), we compute transmission coefficients using the optical model,

J. C. Hardy et at. / T~ _ } ß-delayed proton precursors

35 7

with parameters specifically known to reproduce low-energy scattering data for medium-weight nuclei 2°). Our method for calculating T}, is based on the E1 y-ray strength functionfE,(Ey) . If it is assumed that the levels i decay predominantly by E1 radiation, then with ~rv~E1

tiy,sx

= JOf

E~E1(Ey)

J,+ 1 ~

1=J,-1

Pt(Ex -Ey)

PJ,(Ex)

dEy ,

(4)

where K is an ad hoc correction factor, which should be near 1 .0 if our assumption is correct. The strength function can be related') to the measured cross section for photonuclear absorption in the region of the electric dipole resonance. Previously ' ~'°), we have adopted 16 MeV as the energy of the dipole resonance, and evaluated
The decay of es Ge, determined from this and previous 11,12) work, appears in fig. 1 . In addition, two other properties of excited states between 5 and 6 MeV in 6sGa are known :one has already been described-their average lifetime as manifested in the measured X-ray ratio limit ; the other is their density. The reaction 6aZn(p, y)6sGe has been studied by Leslie Ze) between 1 .4 and 1 .8 MeV proton energy . Experimentally, he counted 59 ± 8 resonances, which, when compared with computer simulations, he concluded corresponds to a total density of states of 1125/MeV at an average excitation energy of 5.5 MeV. This level density disagrees considerably with the Gilbert and Cameron density formula if the Truran et al. 22) parameters are employed. However, if the pairing energy is held fixed at the prescribed 1 .285 MeV, and the level density parameter a is varied, good agreement with the (p, y) result is achieved with a = 10.5 MeV-1

35 8

J. C. Hardy et al. / T_ = i ß-delayed proton precursors

[cf. a = 7.8 MeV- ' predicted in ref. Z~)] . The corresponding proton distribution, calculated according to equations (1 }-(4) with K = 3, is shown as the smooth curve in fg. 1 . Values of K between 1 and 5 would provide equally acceptable representations of the spectrum, but the experimental limit of 0.17 on the zinc-to-gallium X-ray ratio restricts the range to K ~ 3. By comparison, the measured level density agrees more naturally with the predictions of the back-shifted Fermi gas formula. For example, a density parameter a = 8.0 MeV- ' and a "fictive ground state" energy of -0.8 MeV produce agreement with p(Ex = 5.5 MeV) yet lie easily within the expected range of values za) . The proton spectrum calculated with this density also agrees well with the data in fact it is indistinguishable from the calculated distribution already described in fg. 1 - and it does so with K = 1, indicating consistency with the
The decay scheme of'3Kr, determined from this and previous' 3) work, appears in fig. 3. Unlike the case of 65Ge, here the density of states in the emitter (' 3Br) has not been measured directly . However, the coincident X-ray ratio is known in detail' °) as a function of proton energy, and this provides tight constraints on both y-ray widths and level density parameters . The dashed curve in fig. 3 is the statistical model proton distribution calculated from Gilbert and Cameron level densities with parameters determined by fitting the X-ray ratios . This is the same calculation as that shown in ref. 1°), where the determination of these parameters is discussed at some length . The result, though agreeing well with the data, has some unpleasant features . The level density parameter a is significantly different from expectation ss) (13.65 MeV - ' compared with 9.75 MeV- ') and the y-width correction factor, K = 8 .5, is alarmingly large.

J. C. Hardy et ol. / T~ = i ß-delayed proton precursors

35 9

As with 65 Ge, the equivalent calculation with level density taken instead from the back-shifted Fermi gas model appears much more satisfactory . The calculated proton spectrum, shown as the solid curve in fig. 3, agrees at least as well with the data, and furthermore, fits the X-ray ratio distribution [from ref. '°)] with a = 9.2 MeV - ', d = -1 .8 MeV and K = 1 .5. The first two, both density parameters, are comfortably within expectations "), while the latter indicates that the
0* 2* 0* 2*

Branching ratio (~) exp .

talc . ')

82±4

80 .3 17 .1 1 .1 1 .5

18±4 . 5 2

') Calculated assuming' 3ICr to be }* ; the level density in' 3 Br was taken from the back-shifted Fermigas model with parameters as described in the text.

36 0

J . C. tlardy et al. / T = = ß-dela)~ed proton precursors TARLF: 2

Comparison of measured "Kr derdy properties with calculations assuming various J* values for the precursor Property

Experiment

BRP (°. ) BRP ~/(BR w~+BRP ~) (Se/Br) X-ray ratio

0 .68 ±0 .12') 0 .18 f 0 .04 n) 0 .176±0 .012 `)

') Ref. 2) .

n)

This work .

Calculated assuming "Kr spin of

0.03 0.10 0 .19

~*

,+ z

~+

0 .02 0 .18 0 .18

0 .01 0 .22 0 .16

0 .001 0 .69 0 .12

`) Ref.'°) .

While ~+ is preferred, it is not unequivocally so. CErtainly the BRp value does not agree under any circumstances, a difficulty that has already been noted '°) : as the only remaining serious discrepancy, its remeasurement seems indicated. If all protons directly populated the ground state of'ZSe, there would be a oneto-one correspondence between proton energy and excitation energy in ' 3Br ; in that case, the positron-emission intensity to states at a particular energy in '3Br would be determined by the number of coincidences between protons and 511 keV y-rays (Nve) at the corresponding proton energy . The ratio of NPy to NP as a function of proton energy would then reflect the positron-to-total-decay ratio as a function of decay energy ; it would thus be independent of nuclear structure (or the details of the proton spectrum shape) and yield a good measure of the ß+ end point relative to the proton separation energy . In fact, the 18 % proton branch to the first excited state of'ZSe removes the simple correspondence between observed proton energy and excitation energy . However, with the proton branching to the 2+ state in'ZSe well accounted for by our statistical model calculations, we can use the same model to calculate Npß lNP (see fig. 6) and extract a measured value for QEC - BP . This result gains reliability from its relative insensitivity to nuclear structure, while losing precision through the poorer statistics of a coincidence measurement. Our value, QEC- BP = 3 .9 ±0.4 MeV, agrees with, but is less accurate than, the value 3 .70±0.15 MeV obtained from the proton singles spectrum (fig . 3). It is, therefore, the latter value that we quote, noting that the data include those reported in ref. ' ) and so the present value replaces the one quoted there. 5. Conclusions

5 .1 . SPIN-PARITY OF "Kr

As noted in the previous section all known odd nuclei with 37 neutrons have ~ground states . That'3Kr might be an exception need not bP regarded as particularly surprising. The nucleus is in a region of rapidly increasing deformation, whose

!. C . Hardy et al . l T~ _ ~ ß-delayed proton precursors

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40 ~ NEUTRON

50 ~ NUMBER

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PROTON NUMBER

Fig . 7 . (a) Contour diagram of the excitation energies of first excited 2' states in even-even nuclei ; contours are labelled in keV . The T_ = i precursors and their daughters (the emitters) are marked by x . (They are odd-mass nuclei, however, and consequently are otherwise unrelated to the contours) . (b) Energy differences between lowest-energy positive- and negative-parity states in odd-neutron, even proton nuclei . A negative ordinate implies a positive-parity ground state . Each line is labelled by neutron number .

consequence is the dramatic lowering in energy of positive-parity states in odd nuclei z' ~ Z e) . The situation is illustrated in fig. 7. Part a of the figure is a contour diagram of the excitation energy of lowest 2+ states in even-even nuclei throughout this mass region . Superimposed for orientation are the lighter members of the Tz = ~ series of delayed proton precursors, ' 3 Kr being the middle case. Deformation, as evidenced by low-lying 2 + states, is marked in that region . Part b of the figure shows the energy-difference between the lowest positive- and negative-parity states in odd-neutron even-proton nuclei between N = 33 and 41 . The rapid descent of positive-parity states as deformation increases indicates that 36Kr3, could indeed have a positive-parity ground state (a negative ordinate in the graph) without inconsistency. Our result, a ground state spin of ~+ or possibly ~+, would thus be entirely consistent with local systematics. It is also interesting to note that it would be consistent with the weakness of ß-decay to the ground state of' 3Br, which is known ") to be (~, ~, ~) . 5.2 . STATISTICAL MODEL CALCULATIONS

As in previous studies of T= _ ~ precursors r ~' ~ t °), we find that the statistical model is remarkably successful in accounting for the measured properties of ßdelayed proton decay. In this regard the present study has made several important contributions. First, the energy dependence of proton branching [Npl/(N~+NP,)] has been measured and shown to be well-reproduced by calculation ; in fact, it could become a useful tool in determining precursor spin - providing our present

36 2

J. C. Hardy et al. / T-- = i ß-delayed proton precursors TABLE:

3

Summary of mcasured
240 170

330 320

200±60

320±60

Analysis method Gilben-Camcrson p(E.) back-shifted Fermi gas P(E,) adopted values

proposals regarding the JR of' 3 Kr can be confirmed by an independent technique. Second, by choosing cases where the level density is circumscribed by measurement we have been able to show that the back-shifted Fermi gas model is considerably more successful in describing a priori the density of states in exotic nuclei - at least in this mass region - than the prescription of Gilbert and Cameron ; in particular, average y-ray widths seem to be calculable with considerable precision when the back-shifted density formula is used [see also ref. zs)]. Finally, we have shown that the "measured" y-ray widths - i.e. the widths extracted from the data by statistical model analysis - are gratifyingly insensitive to the details of the calculation. This can be seen from table 3 where
5 .3 . ß-DECAY STRENGTH FUNCTION

All TZ = ~ precursors so far studied have been adequately described by a gaussian strength function as employed in the "gross theory" of ß-decay tB .'9) . Such discrepancies as exist in figs. 1 and 3 between experiment and calculation are entirely explainable by fluctuations arising from the (Porter-Thomas) statistical behaviour of Iß and I'P [cf. ref. ae)] . There is no evidence for local nuclear-structure related features in the beta-strength function . We should like to thank Professors K. Eskola and J. R. Leslie for stimulating discussions and useful information.

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