Effective residual neutron-proton interaction in 50Sc and 56Co

PHYSICS

Volume 17, number 2

LETTERS

in the inelastic .channel leading to the first 2+

2. D.Robaon, J.D.Fox, J.A.Beoker, P.Richard, C.F. Moore, D.Long, S.I.Hayakawa, G.VourvoPoulo.9 and C. E. Watson, Florida State University Tandem Accelerator Laboratory, Tech. Report 6, 1964. 3. L. L. Lee, A.Marinov and J. P.Schiffer, Physics Letters 8 (1964) 352. 4. W. Haeberli quoted by H, T . Richarde in Nuclear Spectroacopv. F.Ajzenberp;-Selove ed. (Academic Press, New-York aha Lo&n 1960) vol.i, p. 130. 5. J.M.BlattandL.C.Biedenbarn. Rev.Mod.Phve.24 (1952) 258. 6. H.E.Gove inNuclear Reactions. P.M.Endt and M. Demeur eds . (North-Holland Pub1 . Comp .1959). 7. D.Robson, Phys.Rev. 137 (1965) 535. 8. R.H.Fulmer, A.L.McCarthyandB.L.Cohen, Phys. Rev. 128 (1962) 1302. 9. A.M. Lane, Rev.Mod.Phys.32 (1960) 519,

state in both nuclei. Analysis of the data is in

progress to determine the ;unount of core excitation of the states in 139Ba and 141Ce.

We are indebted to Professor W. Gentner for his interest in this work and his support. We wish to thank Prof. T. Mayer-Kuckuk, Prof. H. Morinaga, Dr. N. Noack and Prof. H. A. WeidenmUller for discussions and Mr. H. Seitz for his help in data taking. References 1. J.D.Fox, C.F.MooreandD.Robaon, Letters 12 (1964) 198.

1 July 1965

Phya.Ftev.

*****

EFFECTIVE

RESIDUAL NEUTRON-PROTON IN 5oSc AND 56Co

INTERACTION

I-I.OHNUMA Department

of Physics,

University

Faculty

of Science,

of Tokyo, Japan

and K. SASAKI Department

of Applied

Physics,

Faculty

of Engineering,

University of Tokyo, Japan Received 1 May 1965

Recently, the low-lying energy levels of 5oSc [l] and 56Co [2] were investigated experimentallJt. The configurations of the last proton and neutron in the ground states of these odd nuclei are predicted by the shell model as (f~)p(p%)n and (fL 1) ‘G&n, respectively. The states J = 2+, 3+, 4 P and 5+ are produced from these configurations. The energy levels of 5OSc were calculated by Vervier [3] who made use of the experimental data of the energy levels of 56Co [4] and the relation of the energy of a particle-particle system with particle-hole one [5] as E(ij’,J)

= - 3

(wt+l)K(ij’j~j;Js)E(i-Ijl,J,).

(1)

The results obtained were 0, 0.025, 0.450 and 0.793 MeV for the states with J=2+, 5+, 3+ and 4+, res ectively. In this analysis, he assumed that in B6~0 the position of the J=5+ level which has not been observed lies at 0.501 MeV. Further126

in ref. 3 the neutron-proton interaction was investigated. It was assumed to be of the form

more,

(2) Vnp = vO[(1-a) + +n’ $16 ( 1‘n- ‘p 1)* The best fit parameters to reproduce the experimental data of the energy levels in 56~0 were given as Fb’o = -0.726 MeV and a=0.063, where Fo is a Slater integral. In ref. 2, similar results were obtained by making use of the new data given in ref. 2. They are FOVO=-0.74 MeV and (Y= 0.078. Calculations with the finite range interaction were carried out in ref. 2 and ref. 6. They assumed also the pure configurations and used the interaction of the form as vnp = vO[(l-or) + +n- up)Jdynp) (3) Here, f(rnp) standsfor the radial dependence of the potential. In ref. 2, the level energies of 56~0 are given by three parameters, i.e. (Y, VOFOand VOF2. These parameters are fitted to

PHYSICS

Volume 17, number 2

0.1

1 July 1965

LETTERS

t 0.2

a3

04

05

08

0.T

0.2

09

IO a

level spacings between 4+ (ground) and 3+ (1st 0.163 MeV), 3+ and 2+ (2nd, 0.975 MeV) of 56Co, and 2+ (ground) and 5+ (lst, 0.025 MeV) of 58Co. The values cr=O.O84, VOF’= -0.80 MeV and VOF2= -3.85 MeV were obtained. In ref. 6 a Gaussian dependence was used for_f(ynp) and the three dimensional isotropic harmonic oscillator wave function was used as one particle wave function. The best fit parameters obtained for 56Co are VO= -42.37 MeV, X (=rO/i u, where r0 is the force range and v = Multi= 0.96A-f x 1026 cme2 [7]) =0.6 (y. = 1.7 fm), and o=O.O7. The calculated energies of the states J = 4+, 3+, 5+ and 2+ are 0, 0.181, 0.484 and 0.984 MeV, respectively. In the above analysis given by several authors, the assumption of the pure configuration was used. For the configuration of the proton, this assumption may be valid since fs orbit forms the

0

0.1

0.2

0.3

0.4

0.5

06

0.7

0.2

0.2

1.0 -

closed shell. For the neutron, however, it is necessary to take into account of the pi and f: orbits in addition to the p$ orbit. Especially, the results obtained by making use of the assumption of the pure configuration cannot predict the levels observed experimentally other than J=2+, 3+, 4’ and 5+ levels. In the present note, the n-p interaction is investigated from the experimental data of the energy levels of 5OSc[ 1] and 56~0 [ 2,8] by taking into account of the configuration mixing for the neutron states as above mentioned. The energies of the single-particle levels are taken from the results of the experiments 48Ca(d, p)4gCa [9] and 58Ni(d, t)57Ni [lo] for 5OSc and 56~0, respectively. Assumed values are AE(p+ - pi) = 2.028 MeV, AE(fg -pi) = 3.95 MeV for the case of 5oSc and AE(p$ -pi) = 1.15 MeV, AE(f$ - p%)= 0.85 MeV 127

PHYSICS

Volume 17, number 2

LETTERS

-.

1 July 1965

Fig. 2. Comparieon of the calculated energy level6 with the experimental ones. Experimental data are taken from ref. 1 for 5oSc and ref. 2 and ref. 8 for 56~0.

oan

l_

t -0

-O.‘w -0

A=i.O

-2*=:oM*V (0)

.m

co”

for the case of 56~0, respectively. The same potential as (3) with Gaussian radial dependence is used for the effective n-p interaction. The results depend considerably on the values of the parameters VO, h and (Y. As an example, in the case of V. = -20 MeV, A = 1.0 and a, is varied from zero to one, the level ordering is shown in fig. 1. The values of the parameters to fit the experimental data of the energy levels of 56Co and 5oS~ are VO=-20 MeV, X=1.0 (~0 x 2.8 fm), a!=0 and VO=-20 MeV, h=l.O, ar=O.O8, respectively and the energy levels obtained with these parameters are shown in fig. 2. As seen from the results, the experimental data of 56co and 5oSc can be explained on the whole with the same values of the parameters. Especially they show that the n-p interaction can be expressed mainly as Wigner force. However, it is noticeable that in 5oSc the ground state cannot be predicted with pure Wigner force (ar=0) (see fig. 2(b)) as well as the assumption of the pure configuration as shown by Vervier [ 31. In the analysis for 56Co, if the 1st 3+ state is adjusted with the experimental data, a negative value of (Yis necessary. In this case the lowest 128

2+ state comes downward, while the lowest 5+ state comes upward and the overall theoretical fitting with experimental data cannot be obtained. In 5OSc, the discussion for the overall fitting is meaningless since only two excited states are experimentally known. The If levels, as seen from fig. 2, lie much higher states and a fit to the experimental data cannot be obtained, so far as the configurations assumed in this note are used. The effects of configuration mixing for the proton such as (pa) (p$)n and (pi),, may be important for the2F + levels as &scussed in ref. 2. As observed in fig. 1, stron mixing occurs for the fitted parameters. In 5ko, the configurations of the last proton and neutron of the ground state are (fr-l) and (pi-l) . If the pure configuration is a&um$d a grkmdn state with same spin and parity as ~OSCis obtained but the ground and 1st excited states of 58Co and 5oSc observed experimentally are J = 2’ (ground), 5+ (0.025 MeV) and J= 5+ (ground), 2+ (0.258 MeV), respectively. This fact indicates the necessity of the consideration of the configuration mixing to study the properties of the effective n-p inter-

Volume 17, number 2

PHYSICS

1 July 1965

LETTERS

4. D.O. Wells, S. L. Blatt and W. E. Meyerhof, Phys.

action in 58Co and 5oSc. The analysis of the effects of the configuration mixing for other odd nuclei is in progress by the present authors.

Rev. 130 (1963) 1961.

5. S. P. Pandya, Phys. Rev. 103 (1956) 956. 6. K. Sass& to be published. 7. H.Noya, A.Arima and H:Horie, Supplementof Prog.Theor.Phys.

No.8 (1958) 33. P.E.Dahl, O.HansenandG.Sidenius, Nuclear Physics 51 (1964) 641. 9. E .Kashy, A.Sperdut.o, H.A.Enge and W. W. Buechner, Phys.Rev. 135 (1964) B865. Phys. 10. M.H.Macfarlane. B.J.RazandJ.L.Yntema, Rev. 127 (1962) 204.

References

8. J.H.Bjerregaard,

1. Y.Shida, M.Ishihara, K.Miysno, HMorinaga and R.Chiba. Phvsics Letters 13 (19&4) 59. 2. H.Ohm&a, Y.Hashimotc and i.Tornita, Nuclear Physics, to be published. 3. J.Vervier, Physics Letters 7 (1963) 200.

DIFFUSION

PARAMETERS

OF LIQUID

HYDROGEN

*

F. A. BRYAN Jr. ASTRA Inc., Raleigh, N.C. and A. W. WALTNER North Carolina

State University,

Raleigh,

N. C.

Received 28 May 1965

Pulsed neutron experiments on liquid hydrogen have been conducted using the North Carolina State 1 MeV Van de Graaff accelerator. These experiments sought to determine the thermal diffusion properties of both ortho- and parahydrogen. Data were accumulated on a 26 channel time analyzer using 10 MSchannel widths. Data accumulation was delayed until moderation was complete and spatial harmonics had died out. This was indicated by the asymptotic approach of the neutron density decay to a pure exponential, and by the ratio of the decay constant measured as a function of time by two counters of different neutron velocity response characteristics. The experimental measurements were made on two para-orthohydrogen mixtures; 95% parahydrogen, 5% orthohydrogen, and 47% parahydrogen, 53% orthohydrogen. The decay constants in the mixture with the high concentration of orthohydrogen were corrected for the decay of ortho- to parahydrogen as a function of time. This decay was determined by measuring the para-ortho ratio throughout the experiment by a device similar to that described by Grilly [I]. Measurements made on the high parahydrogen concentration mixture indicated * This work was supported by the National Aeronautics

and Space Administration under Contract NAS8-2419.

negligible ortho-para conversion over the course of the experiment. Measurements on the high parahydrogen mfxlure were made in a cylindrical geometry of 25.67 cm inside diameter. The axial dimension was varied between 5.0 cm and 21.0 cm. This gave bucklings ranging between 0.03 cmm2 and 0.10 cmm2. Several measurements were taken at each of 15 different bucklings in this range. Measurements on the high orthohydrogen mixture were made in a cylindrical geometry of 16.94 cm inside diameter. The axial dimension in this case was varied between 3.0 cm and 18.0 cm which gave bucklings ranging between 0.10 cmm2 and 0.80 cmm2. Several measurements were made at each of 15 different bucldings in this range. After thermalization and harmonic die-away, neutron density can be described by [2] N = Noemu

where t is elapsed time, No is the initial neutron density and X is the decay constant given by: h=X,

+ DOB2 - C+

(2)

where +, is the infinite medium decay constant, Do is the diffnsion coefficient, C is the diffusion 129