Recent Articles

Beta-decay asymmetry from the decays of oriented ${}^{52}{Mn}$ and ${}^{60}{Co}$

S. T. -C. Hung, K. S. Krane, and D. A. Shirley

Phys. Rev. C 14, 1162 (1976) - Published 1 September, 1976

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The $β$ decay of ${}^{52}{Mn}$ has been investigated by measuring the angular distribution asymmetry of the positrons emitted from ${}^{52}{Mn}$ oriented at low temperatures. The ${}^{52}{Mn}$ nuclei were polarized in an iron lattice and cooled by thermal contact with an adiabatically demagnetized paramagnetic salt. The positron asymmetry was determined by means of two independent techniques: The positrons were detected directly using high-purity germanium detectors and indirectly using NaI detectors to observe the annihilation $γ$ rays. These two techniques yielded a consistent result for the asymmetry, corresponding for this allowed decay to a ratio of the Fermi to Gamow-Teller matrix elements of $y = \frac{C_{V} M_{F}}{C_{A} M_{GT}} = - 0.144 \pm 0.006$ . An auxiliary experiment on ${}^{60}{Co}$ gave a $β$ asymmetry $A = - 0.971 \pm 0.034$ , in excellent agreement with the theoretical value of - 1 expected for maximal parity violation.

RADIOACTIVITY ${}^{52}{Mn}$ , ${}^{60}{Co}$ ; measured $β$ asymmetry, deduced Fermi/ Gamow-Teller ratio in ${}^{52}{Mn}$ decay.

Half-life of ${}^{242}{Pu}$ from precise low-temperature heat capacity measurements

Darrell W. Osborne and Howard E. Flotow

Phys. Rev. C 14, 1174 (1976) - Published 1 September, 1976

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Heat capacity measurements on three pure compounds, ${PuF}_{3}$ , ${PuF}_{4}$ , and ${PuO}_{2}$ , made from 99.91 at.% ${}^{242}{Pu}$ , have been used to evaluate the power produced by radioactive decay. The mean specific power was found to be (0.12099 ± 0.00024) mW per gram of plutonium in the samples. The contribution of nuclides other than ${}^{242}{Pu}$ to the power was calculated to be (5.15 ± 0.11) μW per gram of plutonium, and so the specific power of pure ${}^{242}{Pu}$ is (0.11594 ± 0.00026) ${mWg}^{- 1}$ . A correction for the (5.50 × $10^{- 4}$ )% spontaneous fission branching reduces the specific power due to α decay to (0.11591 ± 0.00026) ${mWg}^{- 1}$ . Combining this value of the specific power with the total disintegration energy of (4.9823 ± 0.0012) MeV we obtain (3.763 ± 0.009) × $10^{5}$ years as the α half-life of pure ${}^{242}{Pu}$ .

RADIOACTIVITY ${}^{242}{Pu}$ ; measured specific power; deduced $T_{\frac{1}{2}}$ .

$g$ factor of the 738 keV state in ${}^{43}K$

S. A. Wender, C. R. Gould, D. R. Tilley, D. G. Rickel, J. D. Turner, and N. R. Roberson

Phys. Rev. C 14, 1179 (1976) - Published 1 September, 1976

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The $g$ factor of the 738 keV second excited state in ${}^{43}K$ has been measured using a perturbed angular correlation technique. A value for the half-life was also obtained. The level was populated via the ${}^{40}{Ar} (α, p) {}^{43}K$ reaction at 15 MeV with a pulsed beam. The spin precession was measured in an external magnetic field of ∼ 3.8 and 5.4 kOe. The measured $g$ factor is + 1.28 ± 0.04, which is consistent with the reported spin of ${7 / 2}^{-}$ . A comparison of the $g$ factor with other ${7 / 2}^{-}$ states in the odd potassium isotopes, and the ground state moments of the odd scandium isotopes reveal the state to be predominantly single particle in nature.

NUCLEAR MOMENTS ${}^{40}{Ar} (α, p)$ , $E_{α} = 15$ MeV, pulsed beam, measured spin rotation in $H = 3.8, 5.4$ , 5.4 kOe, deduced $T_{\frac{1}{2}}$ , $g$ .

Nuclear orientation of ${}^{97, 103, 105}{Ru}$ and ${}^{105}{Rh}$

J. A. Barclay, S. S. Rosenblum, W. A. Steyert, and K. S. Krane

Phys. Rev. C 14, 1183 (1976) - Published 1 September, 1976

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Angular distributions have been measured for $γ$ rays emitted following the decays of ${}^{97, 103, 105}{Ru}$ and ${}^{105}{Rh}$ oriented in an iron matrix at temperatures down to 4 mK. Magnetic moments of the decaying states were deduced to be $| μ ({}^{97}{Ru}) | = (0.687 \pm 0.027) μ_{N}$ , $| μ ({}^{103}{Ru}) | = (0.67 \pm 0.11) μ_{N}$ , $| μ ({}^{105}{Ru}) | < 0.3 μ_{N}$ , and $| μ ({}^{105}{Rh}) | = (4.61 \pm 0.16) μ_{N}$ . Values for the $\frac{E 2}{m 1}$ mixing ratios were deduced for numerous $γ$ rays in the daughter nuclei. The spin assignment of the 442-keV level of ${}^{105}{Pd}$ is deduced to be 7/2.

NUCLEAR MOMENTS ${}^{97, 103, 105}{Ru}$ , ${}^{105}{Rh}$ [from $Ru (n, γ)$ ]; measured $γ (θ)$ from polarized nuclei; ${}^{97, 103, 105}{Ru}$ , ${}^{105}{Rh}$ — deduced nuclear magnetic moment $μ$ ; ${}^{97}{Tc}$ , ${}^{103, 105}{Rh}$ , ${}^{105}{Pd}$ — deduced $\frac{E 2}{M 1}$ $γ$ -ray multipole mixing ratios $δ$ ; ${}^{105}{Pd}$ — deduced spin assignment $I$ .

Coupling of two-quasiparticle and collective excitations in Ge and Zn isotopes

M. Didong, H. Müther, K. Goeke, and Amand Faessler

Phys. Rev. C 14, 1189 (1976) - Published 1 September, 1976

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Excitation energies and $B (E 2)$ values of ${}^{72}{Ge}$ , ${}^{70}{Zn}$ , and ${}^{74}{Ge}$ are investigated by means of an extended generator coordinate method which allows in a microscopic way a simultaneous coupling of single particle and collective degrees of freedom. For the generating wave functions angular momentum and particle number projected Hartree-Fock-Bogoliubov solutions have been used. The low lying states of even parity and angular momentum are dominated by a coupling of shape vibrations and $K = 0$ two-quasiparticle excitations. In contrast to the yrast states especially the anomalously low lying first excited $0^{+}$ state in ${}^{72}{Ge}$ could only be explained by a strong coupling of both degrees of freedom. For ${}^{72}{Ge}$ and ${}^{74}{Ge}$ , the most important contributions are due to the proton excitations, whereas in ${}^{70}{Zn}$ , the neutron excitations play the dominant role.

NUCLEAR STRUCTURE Calculations in Ge and Zn; generator coordinate method; Hartree-Fock-Bogoliubov approach; angular momentum projection; two-quasiparticle states.

Minimization of energy and of energy variance for Slater determinants in nuclei

V. Satyan and J. C. Parikh

Phys. Rev. C 14, 1198 (1976) - Published 1 September, 1976

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Two distinct variational methods for obtaining single determinantal states in light spherical nuclei are studied. The first is the well-known Hartree-Fock method and the second is the minimization of the energy variance method. The equations for determining the self-consistent set of single particle orbits using the new variational procedure are derived. The widths of these states are also evaluated, which provide us with a measure of their departure from the exact eigenstates of the nuclear system. Perturbation theory corrections are also calculated for these determinantal states to estimate the correlation effects. A comparative study of the properties of the Slater determinants using the Hartree-Fock method and the new variational method is also made.

NUCLEAR STRUCTURE Evaluation of variance for Hartree-Fock states, minimization of energy variance for Slater determinants.

Effective particle potentials for Brueckner calculations of finite nuclei

John G. Zabolitzky

Phys. Rev. C 14, 1207 (1976) - Published 1 September, 1976

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From solutions of the Bethe-Faddeev equations we extract effective particle potentials by fitting the factorized ansatz $2 U_{ρ} S_{2}$ to the nonfactorizable three-body amplitude $V χ_{3}$ . It turns out that earlier estimates of a spatially constant potential of about -8 MeV per particle were justified. The smallness of this effective particle potential as compare to the hole potential of -40 MeV indicates the excellent convergence of Brueckner theory for finite nuclei, if the proper generalizations and self-consistency prescriptions of the exp( $S$ ) method are taken into account.

NUCLEAR STRUCTURE ${}^{16}O$ calculated effective particle potential Brueckner-Hartree-Fock method.

Random-phase-approximation ground-state correlations and the isotope effect in the ${}^{40}{Ca}$ and ${}^{48}{Ca}$

E. Tinková and M. Gmitro

Phys. Rev. C 14, 1213 (1976) - Published 1 September, 1976

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Ellis's method of constructing the random-phase-approximation ground-state wave function which avoids the earlier dubious and incorrect quasiboson approximation is extended to the $N \neq Z$ nuclei. The most important effects arise from the appropriate treatment of the isospin quantum number. In application to the calcium isotopes we find that the calculated relative shift of the proton rms radius from ${}^{40}{Ca}$ to ${}^{48}{Ca}$ $R = - 0.35 %$ for the first time agrees with the high energy electron scattering result $R = - 0.31 %$ . Excellent agreement is also obtained for the difference of the neutron and proton rms radii in ${}^{48}{Ca}$ . It should be emphasized, however, that our conclusions concerning the magnitude of the effects on the rms radii due to ground state correlations are more significant than the detailed comparison with experiment.

NUCLEAR STRUCTURE ${}^{40, 48}{Ca}$ ; calculated spectra, shell breaking, rms radii, and density distributions. Ground-state correlations and isospin projection.

Two-quasiparticle-plus-rotor bandmixing calculations of Coriolis decoupling

C. Flaum and D. Cline

Phys. Rev. C 14, 1224 (1976) - Published 1 September, 1976

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Two-quasiparticle-plus-rotor bandmixing calculations have been performed to ascertain whether they can reproduce the phenomena of backbending and anomalous negative parity bands which have been observed in several even-even nuclei. The consequences of this model are discussed in detail for ${}^{156}{Er}$ and some results for ${}^{104}{Pd}$ are presented. The calculations reproduce the observed spectra and electromagnetic decay properties demonstrating the importance of the Stephens and Simon decoupling model. A new coupling scheme clearly emerges, for high-spin two-quasiparticle states at intermediate deformation, where both the magnitude of the intrinsic spin of the particles and its projection on the axis of rotation are approximately good quantum numbers. The residual two-quasiparticle interaction has been shown to have little influence on the high-spin behavior.

NUCLEAR STRUCTURE ${}^{156}{Er}$ and ${}^{104}{Pd}$ ; calculated $E_{x}$ , wave functions, and electromagnetic properties of two-quasiparticle bands; demonstrated the applicability of the Coriolis decoupling model.

${}^{4}{He} - d - d$ vertex constant and normalization

T. K. Lim

Phys. Rev. C 14, 1243 (1976) - Published 1 September, 1976

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The ${}^{4}{He} - d - d$ vertex constant, extracted from direct and parametrization methods, is found to yield $C^{2} \approx 50$ . A comparison of this with observed values from transfer reactions and $d - {}^{4}{He}$ elastic scattering suggests a normalization $P_{d - d}$ of 0.5.

NUCLEAR STRUCTURE ${}^{4}{He}$ ; calculated $d - d$ vertex constant, normalization.

Structure of low-lying positive-parity states of ${}^{18}O$

R. L. Lawson, F. J. D. Serduke, and H. T. Fortune

Phys. Rev. C 14, 1245 (1976) - Published 1 September, 1976

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Data on single-nucleon transfer, ( $t, p$ ) cross sections, and static and dynamic electromagnetic properties place severe limitations on the structure of the low-lying positive-parity states of ${}^{18}O$ . We deduce wave functions that best reproduce these data by use of a model space that includes one collective state each of spin $0^{+}$ , $2^{+}$ , and $4^{+}$ together with all basis states formed from a closed ${}^{16}O$ core plus two $d_{\frac{5}{2}}$ , $s_{\frac{1}{2}}$ neutrons and up to one $d_{\frac{3}{2}}$ neutron. There is need for only a small $d_{\frac{3}{2}}$ admixture. The $0^{+}$ collective configuration is the dominant constituent of the $0_{2}^{+}$ state at 3.63 MeV, and the $2^{+}$ collective configuration dominates the $2_{3}^{+}$ state at 5.25 MeV. Overall, the data favor a small negative value ( $\frac{Q}{e} ≃ - 5$ ${fm}^{2}$ ) for the quadrupole moment of the first $2^{+}$ level. The matrix elements of the Hamiltonian that reproduce both the observed energies and transition rates are constructed. Several experiments are suggested to further probe the structure of this nucleus.

NUCLEAR STRUCTURE Deduce wave functions of ${}^{18}O$ low-lying states that best fit single-nucleon transfer, ( $t, p$ ) data, and static and dynamic electromagnetic properties. Construct Hamiltonian that leads to these eigenfunctions.

Momentum distributions in the nucleus

R. D. Amado

Phys. Rev. C 14, 1264 (1976) - Published 1 September, 1976

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The power law falloff of the nuclear form factor $F (q)$ and single particle momentum distribution $n (q)$ for large $q$ are discussed. For $F (q)$ we show that it is $\frac{q}{A}$ that must be large for the asymptotic form to be valid. In a one-dimensional model with $δ$ function forces the form factor is shown to fall exponentially with $q$ if $q$ is large but $\frac{q}{A}$ is not. Similar behavior is suggested for $n (q)$ .

NUCLEAR STRUCTURE Large momentum behavior of nuclear form factor and single particle momentum distribution in general and in a one-dimensional model.

Overlapping $10^{+}$ and $12^{+}$ resonances near $E_{c . m .} = 18.5$ MeV in ${}^{12}C$ + ${}^{12}C$

H. T. Fortune, S. C. Headley, L. R. Medsker, T. H. Braid, R. E. Segel, and K. Raghunathan

Phys. Rev. C 14, 1271 (1976) - Published 1 September, 1976

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The confusing situation near $E_{c . m .} = 18.5$ MeV in ${}^{12}C$ + ${}^{12}C$ can be understood as arising from the presence of overlapping $10^{+}$ and $12^{+}$ resonances, both of which are exhibited in ${}^{12}C ({}^{12}C, α) {}^{20}{Ne} (g . s .)$ . The presence of both in ${}^{12}C$ ( ${}^{12}C$ , ${}^{8}{Be}$ ) ${}^{16}O$ (g.s.) has been previously reported by Fletcher et al.

NUCLEAR REACTIONS ${}^{12}C ({}^{12}C, α)$ , $E = 36.6 - 37.5$ MeV; measured $σ (E, θ)$ . Legendre polynomial fits.

Comment on ${}^{13}C (π^{+}, π^{0}) {}^{13}N_{g . s .}$ in the (3, 3) resonance region

A. Gal and J. M. Eisenberg

Phys. Rev. C 14, 1273 (1976) - Published 1 September, 1976

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RAPID COMMUNICATION

Low-lying positive parity states in deformed Cs nuclei

K. Sofia, B. P. Pathak, and S. Das Gupta

Phys. Rev. C 14, 1277(R) (1976) - Published 1 September, 1976

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RAPID COMMUNICATION

Backscattering of $α$ particles by light nuclei

H. T. Coelho, F. A. B. Coutinho, and A. F. R. de Toledo Piza

Phys. Rev. C 14, 1280(R) (1976) - Published 1 September, 1976

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RAPID COMMUNICATION

Half-life measurement of the 57.6-keV level in ${}^{127}I$

Suvra Sanyal, Ashok Kumar, S. K. Soni, S. L. Gupta, and S. C. Pancholi

Phys. Rev. C 14, 1285(R) (1976) - Published 1 September, 1976

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RAPID COMMUNICATION

Ratio of neutron capture cross sections for ${}^{186}{Os}$ and ${}^{187}{Os}$ at 25-keV neutron energy

J. C. Browne, G. P. Lamaze, and I. G. Schroder

Phys. Rev. C 14, 1287(R) (1976) - Published 1 September, 1976

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The ratio of the neutron capture cross sections for ${}^{186}{Os}$ and ${}^{187}{Os}$ was measured at the 25-keV iron-filtered neutron beam facility of a 10-MW reactor. A value of 0.41 ± 0.04 was obtained. Using this ratio, the age of the universe was determined via the Re-Os $β$ -decay clock to be approximately 19 × $10^{9}$ years.

NUCLEAR REACTIONS ${}^{186, 187}{Os} (n, γ)$ , $E_{n} = 25$ keV, measured cross-section ratio.

Particle unbound states in ${}^{29}{Si}$ and ${}^{29}P$ by the reaction ${}^{28}{Si} (d, p n)$

C. M. Teodorescu, P. Viatte, S. Micek, R. Müller, J. Lang, J. Unternährer, and L. Jarczyk

Phys. Rev. C 14, 775 (1976) - Published 1 September, 1976

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Stripping reactions to unbound states in ${}^{29}P$ and ${}^{29}{Si}$ were investigated by measuring proton-neutron angular correlations. Similar to stripping experiments which include the measurement of the polarization of the incoming or outgoing particle, this method allows assignments of spins, parities, and partial widths of highly excited levels. The applicability of this method was tested for the case of ${}^{29}P$ , where information is available from proton scattering. Also, several new assignments were possible for unstable levels of ${}^{29}{Si}$ . For the analysis of the data a distorted-wave Born-approximation program for the calculation of transfer reactions to unbound states was developed.

NUCLEAR REACTIONS ${}^{28}{Si} (d, p) {}^{29}{Si} (n) {}^{28}{Si}$ and ${}^{28}{Si} (d, n) {}^{29}P (p) {}^{28}{Si}$ , $E = 11$ MeV. Measured $σ (E_{p}, θ_{p}, θ_{n})$ ; DWBA analysis; deduced particle-unbound levels in ${}^{29}{Si}$ and ${}^{29}P$ , $J$ , $π$ , $Γ$ .

Separable expansions for local potentials with Coulomb interactions

Sadhan K. Adhikari

Phys. Rev. C 14, 782 (1976) - Published 1 September, 1976

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If two particles are interacting via a short range potential and a repulsive Coulomb potential the $t$ matrix can be written as a sum of the Coulomb and the "nuclear" $t$ matrices. In order to solve the three-nucleon problem with Coulomb interactions usually we need a separable representation of this nuclear $t$ matrix. A recently proposed method for finding a separable expansion for local potentials is here extended to find a rapidly convergent separable expansion, with analytic form factors, for the nuclear part of the $t$ matrix of a local potential, in the presence of Coulomb interactions. The method is illustrated for a two-term Malfliet-Tjon potential. In each rank the nuclear phase shift is close to the corresponding phase shift when the Coulomb interaction is switched off.

NUCLEAR REACTIONS Finite rank approximations to the $t$ matrix of local potential considered in presence of Coulomb interactions, $t$ matrices, phase shifts calculated at different energies.

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Beta-decay asymmetry from the decays of oriented ${}^{52}{Mn}$ and ${}^{60}{Co}$

Half-life of ${}^{242}{Pu}$ from precise low-temperature heat capacity measurements

$g$ factor of the 738 keV state in ${}^{43}K$

Nuclear orientation of ${}^{97, 103, 105}{Ru}$ and ${}^{105}{Rh}$

Coupling of two-quasiparticle and collective excitations in Ge and Zn isotopes

Minimization of energy and of energy variance for Slater determinants in nuclei

Effective particle potentials for Brueckner calculations of finite nuclei

Random-phase-approximation ground-state correlations and the isotope effect in the ${}^{40}{Ca}$ and ${}^{48}{Ca}$

Two-quasiparticle-plus-rotor bandmixing calculations of Coriolis decoupling

${}^{4}{He} - d - d$ vertex constant and normalization

Structure of low-lying positive-parity states of ${}^{18}O$

Momentum distributions in the nucleus

Overlapping $10^{+}$ and $12^{+}$ resonances near $E_{c . m .} = 18.5$ MeV in ${}^{12}C$ + ${}^{12}C$

Comment on ${}^{13}C (π^{+}, π^{0}) {}^{13}N_{g . s .}$ in the (3, 3) resonance region

Low-lying positive parity states in deformed Cs nuclei

Backscattering of $α$ particles by light nuclei

Half-life measurement of the 57.6-keV level in ${}^{127}I$

Ratio of neutron capture cross sections for ${}^{186}{Os}$ and ${}^{187}{Os}$ at 25-keV neutron energy

Particle unbound states in ${}^{29}{Si}$ and ${}^{29}P$ by the reaction ${}^{28}{Si} (d, p n)$

Separable expansions for local potentials with Coulomb interactions

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