Investigation of the validity of the valence model for neutron capture in the mass range 40 < A < 70

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Investigation of the validity of the valence model for neutron capture in the mass range 40 < A < 70

H. Beer

To cite this version:

H. Beer. Investigation of the validity of the valence model for neutron capture in the mass range 40 < A < 70. Journal de Physique, 1979, 40 (4), pp.339-342. �10.1051/jphys:01979004004033900�.

�jpa-00209114�

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LE JOURNAL ^DE

PHYSIQUE

Investigation ^{of the} validity ^of^the valence model ^for ^neutroncapture

in the mass range 40 A 70

H. Beer

Kernforschungszentrum ^Karlsruhe^GmbH,Institut für Angewandte Kernphysik, Postfach 3640, ^D-7500Karlsruhe, F.R.G.

(Reçu ^le¹⁹^octobre^1978,accepté le 29 novembre 1978)

Résumé. ²⁰¹⁴Pour un grand ^{nombre de}^noyaux^{dans la}région ^3s(40 ^A 70) ^étudiésexpérimentalement ^à

l’accélérateur pulsé ^Vande Graaff 3 MV de Karlsruhe, ^leslargeurs totales de photon ^sontcalculées à l’aide du modèle de valence et comparées âvecles résultats expérimentaux. ^Lavalidité de ce modèle est examinée de façon systématique. ^Nous^trouvons^{que la}capture de valence joue ^seulementûnrôle limité dans la région ⁴⁰ Â ^70.

Abstract. ²⁰¹⁴For a large number of nuclei in the 3s giant ^resonanceregion (40 ^A 70) ^studiedexperimentally

at the Karlsruhe pulsed ^{3 MV}Van de Graaff accelerator total radiation widths have been calculated by ^means^of

the valence capture ^{model and}compared ^{with the}experimental ^results.Systematic trends of the validity ^{of this}

model have been investigated. ^It ^wasfound that valence capture plays only ^alimited role in the mass

region ⁴⁰^A ^70.

Classification Physics ^Abstracts

24.30

1. Introduction. - The capture ^and^total^cross- sections for a considerable number of nuclei in the

mass range of the 3s giant ^resonance(40 ^A 70)

have been measured [1-4] ^at^the^Karlsruhepulsed

3MV Van de Graaff accelerator. In the analysis ^of

the s-wave resonances significant correlations between reduced neutron widths and total radiation widths have been detected [1] ⁱⁿcontrast to the expectations

of the model of compound nucleus formation.

Correlations of this type ^arefrequently ^associated

with a single particle capture mechanism, namely

the valence capture [5, 6] which should exhibit strong high energy El transitions from Sl/2 states to low

lying 2P1/2,3/2 ^levels. ^According^to^the^model^the partial radiation widths of these transitions can easily

be calculated by ^means^ofexperimentally ^determined

resonance neutron widths and (d, p)-spectroscopic

factors of the final states. The total radiation widths of the resonances are then obtained by ^a^summation

over all partial radiation widths of these high energy transitions.

2. Calculation of valence capture. ^-^{In the}present investigation ^total^radiation^widths^were^calculated

via the valence model for the various nuclei which have been studied experimentally ^at^the^Karlsruhe

3 MV Van de Graaff accelerator. The calculations

were carried out using ^the ^formulae given by Cugnon [7]. ^Forspin ^zerotarget ^nuclei^the^total

radiation width rv of valence capture ^isgiven by ^the expression :

Z and A are charge ^and^mass^number^of^the^residual nucleus, kn ^{is the}^neutron^wavenumber, Tn ^the

neutron width, Ojf ^the^final^state^widthôr^(d,^p) spectroscopic ^{factor of}^{a state}^f^withspin j, ê^the^cor- responding gamma-transition energy ^tothis state f, A(jf) ân angular coupling ^constantândJ(jj,jf)

contains the radial overlap integral of initial and final state wave functions.

The calculations according ^toeq. (1) ^were^carried

out using ^the^measured^neutron^widths^{and the}(d, p) spectroscopic ^factors given in literature together

with the tabulated values of the quantity 1 J 1 ^from Cugnon [7]. Concerning ^thecalculation of the total radiation widths for 5 3Cr it has to be noted that the (d, p) spectroscopic ^factors^takenfrom refe-

rence [8] ^wererenormalized. This appeared ^to^be justified âsâll(d, p) spectroscopic factors for the various nuclei given ⁱⁿ^reference[8] âresystematically

lower than the results of other measurements.

In figures ¹^and²the theoretical and experimental

results for the s-wave resonances of the individual

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01979004004033900

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340

Fig. ^1.^-Comparison of experimental ^andtheoretical total radiation widths for the even-even nuclei of Cr, Fe and Ni (experimental ^{values :}

hatched bars, theoretical values : white bars). ^For^each^nucleus^thebinding energy EB and for each resonance the neutron energy E. ^are specified.

Fig. ^2.^-Comparison ^ofexperimental ^andtheoretical total radiation widths of the odd target ^nuclei47Ti, 59Co, 53Cr, 57Fe and 61 Ni (experi-

mental values : hatched bars, theoretical values ; white bars). ^{For each}nucleus the binding energy EB ând^thespin Î^{and for}êach^reso-

nance the neutron energy Eu ^{and the}compound ^nucleusspin ^J^arespecified.

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values are represented by ^white^and^hatchedbars, respectively. ^Forresonances located below the 5 keV energy limit of the Van de Graaff accelerator, experi-

mental values from other work were included. The

experimental results of 54Cr were taken from Stieglitz

et al. [9].

3. Discussion. ^-The comparison ^ofcalculation and measurement shows that in some cases valence capture ^seems^to^beresponsible ^foressentially ^all^the

observed radiation widths. In addition the existence of a threshold effect in neutron energy is indicated.

For the neutron deficient nuclei 54Fe, ^5°Cr^and

58Ni the agreement between theoretical and experi-

mental values is _verygood up ^toabout 100 keV

resonance energy (Fig. 1). The transition to more

neutron rich nuclei which is connected with a reduc- tion in excitation _energyseems to lower this neutron energy threshold so that for the neutron richest nuclei 54Cr, ^5"Fe^and^64Ni^themodel totally ^fails

to yield ^theexperimental radiation widths. A threshold behaviour for valence capture ^hasalready ^been predicted by Cugnon and Mahaux [6].

Among ^thestudied odd target ^nuclei(Fig. 2) ^53Cr

and 57Fe seem to be good candidates for a valence model capture mechanism. S9Co and 6’Ni show sizeable valence capture only ^forsome resonances

with large ^neutron^widths^whereas^for^the^{47 Ti}

resonances the valence model fails.

A further check of the validity ^of^the^valence

model consists in the study ^ofhigh energy transitions of individual s-wave resonances. These studies can be carried out in some special ^caseswith thermal neutrons if the thermal cross-section is primarily ^due^to^the

tail of a nearby ^s-waveresonance. In this _{way the}

validity of the valence model has been confirmed for the 5.64 keV resonance in 5°Cr [10] ^{and for}^the

7.67 keV resonance in 54Fe [11]. ^At^ourlaboratory partial radiation widths of high energy transitions for the 27 keV resonance in 56Fe, ^the ^{13.3 keV}

resonance in 6°Ni and the 15.4 and 63 keV resonances

in S8Ni have been measured [12]. ^{In these}^cases^the

valence model _appearsto predict only ^{for the}^6°Ni

resonance at 13.3 keV the measured widths. The theoretical values for 56Fe and S8Ni are much higher

than the experimental ^results.Figure 3 shows the

comparison ^betweentheoretical and measured widths for the two 58Ni resonances and for the 13.3 keV

resonance in 6°Ni.

4. Conclusions. - Among ^the ^even-even target nuclei of Cr, ^{Fe and}Ni, 5°Cr, ^54Fe^and^6°Ni^show

Fig. ^3.^-Comparison of calculated and measured partial ^radiation

widths for high energy transitions of the 13.3 keV 6°Ni resonance

(below) ^{and the}¹⁵^{keV and}⁶³^keVresonances in 58Ni (above) (experimental values : hatched bars, theoretical values : white bars). For each nucleus the high energy transitions are indicated.

dominant valence capture. ^Furthercandidates for valence capture ^are^{57 Fe}^and53Cr, however, high

energy transitions of individual resonances should be studied. A threshold effect for the validity ^{of valence}

capture ^seems^to^bepresent ^asit is indicated by ^the comparison of theoretical and experimental ^data.

This effect has already ^beenpredicted by Cugnon

and Mahaux [6]. ^{Most of}^thestudied nuclei do not show the expected strong ^valencecapture ^so^that this mechanism plays only ^alimited role in the 40 A 70 mass range.

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342

References [1] BEER, ^{H. and}SPENCER, ^R.R., Nucl. Phys. ^A²⁴⁰(1975) ^29.

[2] FRÖHNER, ^F.H., ^KfK-2046(1973).

[3] SPENCER, ^{R. R. and}BEER, H., ^Nucl.^Sci.Eng. ⁶⁰(1976) ^390.

[4] HONG, ^L.D., BEER, H., KÄPPELER, F., Specialists Meeting ^on

Neutron Data of Structural Materials for Fast Reactors, CBNM Geel, December 1977.

[5] LYNN, J. E., Theory of Neutron Resonance Reactions (Oxford

Clarendon Press) ^1968.

[6] CUGNON, ^{J. and}MAHAUX, C., ^Ann.Phys. ⁹⁴(1975) ^128.

[7] CUGNON, J., ^Nucl.Phys. ^A²⁶³(1976) ^61.

[8] BOCHIN, V. P., ZHEREBTSOVA, K. I., ZOLOTAREV, ^V.S., KOMAROV, ^V. A., KRASOV, ^L. V., LITVIW, ^V. F.,

NEMILOV, ^Yu.A., NOVATSKY, ^B.G., PISKORZH, Sh., Nucl. Phys. ⁵¹(1964) ^161.

[9] STIEGLITZ, ^R.G., HOCKENBURY, ^R.W., BLOCK, ^R.C., ^Nucl.

Phys. ^A¹⁶³(1971) ^592.

[10] MUGHABGHAB, ^S.F., Proc. of ^theConf. Nucl. Structure Study with Neutrons, Budapest, 1972, Eds. J. Erô and J. X. Szucs (Plenum Press, ^N.Y.) 1974, p. 167.

[11] MUGHABGHAB, ^S.F., Proc. of the ^2nd^Int.Symp. ^on^Neutron Capture Gamma-Ray Spectr. and Related Topics, Petten, 1974, p. 53.

[12] BEER, H., SPENCER, ^R.R., KÄPPELER, F., Z. Phys. ^{A 284} (1978) 173.