Recent Articles

Effective cross sections for the ( $n, 2 p n$ ), ( $n, 2 p$ ), and ( $n, 3 p n$ ) reactions using intermediate-energy neutrons

John C. Hill, D. G. Shirk, R. F. Petry, and K. H. Wang

Phys. Rev. C 12, 1978 (1975) - Published 1 December, 1975

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"Effective cross sections" for the ( $n, 2 p n$ ), ( $n, 2 p$ ), and ( $n, 3 p n$ ) reactions on various targets were measured relative to the ${}^{12}C (n, 2 n) {}^{11}C$ reaction. The bombarding particles were the spectrum of neutrons generated in a Cu beamstop by 750-MeV protons. The cross section systematics as a function of target mass number are compared with available 14-MeV neutron cross sections for ( $n$ , ${}^{3}{He}$ ) and ( $n, 2 p$ ) reactions and with results from intranuclear-cascade calculations.

NUCLEAR REACTIONS ${}^{31}P$ , ${}^{45}{Sc}$ , ${}^{51}V$ , ${}^{75}{As}$ , ${}^{115}{In}$ , ${}^{127}I$ , ${}^{133}{Cs}$ , ${}^{142}{Ce}$ , and ${}^{197}{Au} (n, 2 p n)$ ; ${}^{45}{Sc}$ , ${}^{89}Y$ , ${}^{127}I$ , ${}^{133}{Cs}$ , and ${}^{139}{La} (n, 2 p)$ ; ${}^{31}P$ , ${}^{41}K$ , ${}^{75}{As}$ , ${}^{115}{In}$ , and ${}^{138}{Ba} (n, 3 p n)$ ; $E_{n} = 0 - 750$ MeV; measured $σ$ .

Calculation of the covariant pion-nucleus optical potential. I. Kinematical aspects

L. Celenza, L. C. Liu, and C. M. Shakin

Phys. Rev. C 12, 1983 (1975) - Published 1 December, 1975

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A discussion of several kinematical schemes used in the study of pion-nucleus scattering is presented. It is shown that various kinematical ambiguities of the noncovariant theories are resolved in a covariant analysis. In particular, the use of an off-mass-shell description for the projectile and the target particles provides a degree of freedom in the kinematical description which avoids various problems present in the noncovariant analyses. We present a comparison of the angle transformations, matrix elements, and differential cross sections obtained from the different kinematical specifications. In these comparisons we have attempted to maintain a clear separation of the dynamical and kinematical assumptions, using the same pion-nucleon interaction in all the cases considered. It is found that the large angle scattering is most sensitive to the details of the kinematical description.

NUCLEAR REACTIONS Scattering theory, pion optical potential, comparison of kinematic transformations.

Longitudinal electron polarization for a second-forbidden beta decay

Duane R. Doty and Earle I. Neill, Jr.

Phys. Rev. C 12, 1994 (1975) - Published 1 December, 1975

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Electron polarization from the second-forbidden $β$ decay in ${}^{137}{Cs}$ has been investigated by use of a lens spectrometer. Møller scattering from a hydrogen-annealed Supermendur foil of 2 × $10^{- 2}$ mm thickness was employed to measure the polarization. Fast-slow coincidence techniques were used. Solid state detectors, a small area scattering foil, and a highly collimated spectrometer defined the scattering geometry and helped to reduce background. Analysis of the data was performed from a two-parameter recording to eliminate chance coincidence events. Two independent techniques of measurement resulted in $P_{e} = - 1.0 \pm 0.2$ . A substantial deviation from the value of $P_{e} = - \frac{v}{c} = 0.92$ , which would be expected for allowed decays, was not observed.

RADIOACTIVITY ${}^{137}{Cs}$ ; Møller scattering, measured electron polarization of second-forbidden decay.

Gamma-ray angular distributions and parity tests in the decays of polarized ${}^{173}{Lu}$ and ${}^{174}{Lu}^{m, g}$

K. S. Krane, C. E. Olsen, S. S. Rosenblum, and W. A. Steyert

Phys. Rev. C 12, 1999 (1975) - Published 1 December, 1975

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Angular distributions of 18 $γ$ rays have been measured following the decays of ${}^{173}{Lu}$ and ${}^{174}{Lu}^{m, g}$ polarized at low temperatures in the ferromagnetic cubic Laves-phase metal Zr ${Fe}_{2}$ . The magnetic moments of the oriented parent states are deduced to be $| μ ({}^{173}{Lu}) | = (2.34 \pm 0.09) μ_{N}$ , $| μ ({}^{174}{Lu}^{g}) | = (1.94 \pm 0.28) μ_{N}$ , and $| μ ({}^{174}{Lu}^{m}) | = (2.34 \pm 0.33) μ_{N}$ . The spin of the 1518-keV level of ${}^{174}{Yb}$ is shown unambiguously to be 6. Multipole mixing ratios are deduced for a number of ${}^{173}{Yb}$ and ${}^{174}{Yb}$ $γ$ rays, and several interband $\frac{E 2}{M 1}$ mixing ratios are compared with values deduced from a Coriolis mixing calculation. The 0°-180° asymmetries of the angular distributions of some of the strongly hindered ${}^{174}{Yb}$ transitions have been observed in a search for the presence of parity mixing effects; no such effects were seen. A possible empirical correlation between $γ$ -ray hindrance and the magnitude of parity-violating effects is pointed out.

RADIOACTIVITY ${}^{173}{Lu}$ , ${}^{174}{Lu}^{m}$ , ${}^{174}{Lu}^{g}$ ; measured $γ (θ)$ from polarized nuclei; deduced magnetic moment $μ$ , $γ$ -ray multipole mixing ratios, $δ (\frac{E 2}{M 1})$ , $δ (\frac{E 2}{E 1})$ , $δ (\frac{E 3}{E 1})$ , $g_{K}$ , $g_{R}$ , $J$ , Coriolis mixing, no observable parity violation.

Two-particle, one-hole states in antimony nuclei and the decay of ${}^{121}{Te}^{m, g}$

R. A. Meyer, R. G. Lanier, and J. T. Larsen

Phys. Rev. C 12, 2010 (1975) - Published 1 December, 1975

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The decay of ${}^{121}{Te}^{m, g}$ and the concomitant $γ$ rays from levels of ${}^{121}{Sb}$ have been measured. The decay of ${}^{121}{Te}^{g}$ is found to populate levels at ( $\frac{J^{π}}{log ft}$ value given in parentheses) 507.59 keV ( $\frac{\frac{3}{2^{+}}}{6.87}$ ) and 573.14 keV ( $\frac{\frac{1}{2^{+}}}{6.11}$ ), while the decay of ${}^{121}{Te}^{m}$ is found to populate levels at g.s. ( $\frac{\frac{5}{2^{+}}}{-}$ ), 37.138 keV ( $\frac{\frac{7}{2^{+}}}{log f_{1} t} = 9.63$ ), 946.99 keV ( $\frac{\frac{9}{2^{+}}}{9.93}$ ), 1024 keV ( $\frac{\frac{7}{2^{+}}}{log f_{1} t} \geq 12.35$ ), 1035.53 keV ( $\frac{\frac{9}{2^{+}}}{9.70}$ ), 1139.29 keV ( $\frac{\frac{11}{2^{+}}}{7.85}$ ), and 1144.65 keV ( $\frac{\frac{9}{2^{+}}}{11.19}$ ). These levels and their decay properties are found to be described well by recent calculations which include two-particle, one-hole configurations (2p-1h). Decay of the 2p-1h $½^{-}$ and $\frac{3}{2^{-}}$ levels in ${}^{119}{Sb}$ populated in the decay of ${}^{119}{Te}$ are also presented.

RADIOACTIVITY ${}^{121}{Te}^{m, g}$ , measured $E_{γ}$ , $I_{γ}$ ; deduced $Q$ value, $log ft$ , ${}^{121}{Sb}$ levels: Compton suppression spectrometer.

Magnetic moment of the $I^{π} = {\frac{25}{2}}^{-}$ isomer in ${}^{179}{Hf}$ and anomalous orbital proton $g$ factor

H. Hübel, K. Freitag, E. Schoeters, R. E. Silverans, L. Vanneste, and R. A. Naumann

Phys. Rev. C 12, 2013 (1975) - Published 1 December, 1975

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The magnetic moment of the $I^{π} = {\frac{25}{2}}^{-}$ isomeric state at 1106 keV in ${}^{179}{Hf}$ was measured by the technique of low-temperature nuclear orientation. From the result $μ (\frac{25}{2}) = (7.43 \pm 0.34) μ_{N}$ the value $g_{l} = 1.08 \pm 0.05$ for the effective proton $g_{1}$ factor is deduced.

RADIOACTIVITY ${}^{179}{Hf}^{m}$ , ${}^{177}{Lu}$ . Measured $γ (⊖)$ polarized nuclei, $γ γ (⊖, H)$ . Deduced $δ$ , $μ H$ , $ω τ$ , $μ$ , $g_{l}$ . ${}^{3}{He}$ / ${}^{4}{He}$ refrigerator, Ge(Li) detectors.

Second class interactions and the electron-neutrino correlation in nuclear beta decay

Frank P. Calaprice

Phys. Rev. C 12, 2016 (1975) - Published 1 December, 1975

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The electron-neutrino correlation for ${}^{6}{He}$ $β$ decay is analyzed for possible second class effects. Existing data are found to be consistent with there being no second class form factor but the conclusion is somewhat model dependent. The $e ν$ correlation for the ${}^{19}{Ne}$ decay is considered and it is shown that an improved measurement, comparable to that achieved for ${}^{6}{He}$ , would provide an unambiguous result concerning second class terms.

RADIOACTIVITY ${}^{6}{He}$ ; deduced second class form factor from the $e ν$ angular correlation.

Determination of the sign and magnitude of the nuclear quadrupole interaction by $β - γ$ directional correlations

R. S. Raghavan, P. Raghavan, and E. N. Kaufmann

Phys. Rev. C 12, 2022 (1975) - Published 1 December, 1975

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Experiments are reported which demonstrate that the sign and magnitude of the quadrupole interaction of excited nuclear states can be reliably determined by means of time-differential $β - γ$ directional correlations with radioactive sources embedded in noncubic single crystals. The 828 keV leyel of ${}^{115}{In}$ and the 247 keV level of ${}^{111}{Cd}$ , fed by an allowed and a unique first-forbidden $β$ decay, respectively, have been investigated by this method. The coupling constants $\frac{e^{2} qQ}{h}$ of these levels in Cd metal at 298°K, are -146(5) MHz for ${}^{115}{In}$ and +125(4) MHz for ${}^{111}{Cd}$ . The positive coupling constant for ${}^{111}{Cd}$ in Cd coupled with a positive quadrupole moment $Q$ of this level implies a positive electric field gradient in Cd confirming recent theoretical predictions. The negative $e^{2} qQ$ for the ${}^{115}{In}$ level in Cd metal correspondingly indicates a negative $Q$ for this level in conformity with its description as a member of a $K = \frac{1}{2}$ rotational band. The paper includes a discussion of the major concepts underlying the various methods available now for determination of the sign of $e^{2} qQ$ . Also, a detailed account of theoretical formulas necessary to evaluate allowed and forbidden $β - γ$ perturbed angular correlations and a brief discussion of the significance of the technique for further studies of nuclear quadrupole effects in materials are given.

RADIOACTIVITY ${}^{115}{Cd}^{m}$ , ${}^{111}{Ag}$ ; measured $β - γ (θ)$ in Cd single crystal; deduced ${}^{115}{In}$ , ${}^{111}{Cd}$ levels $e^{2} qQ$ and sign in Cd.

Solidification of neutron matter

V. Canuto and J. Lodenquai

Phys. Rev. C 12, 2033 (1975) - Published 1 December, 1975

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A new parity-conserving equation of motion is used to evaluate the ground state of a system of high density neutrons in a quantum crystal. If one form of a purely repulsive $NN$ potential is employed, the ground state energy has a minimum with respect to the localization parameter in the density range appropriate to neutron star interiors, whereas it does not if a realistic $NN$ potential is used. However, the values of the localization parameters ${α_{m}}^{- 1}$ corresponding to the observed minima are very close to or even less than the separation $Δ$ between neutrons. Since the method employed here for the solid is only reliable when $α_{m} Δ > 1$ , one cannot definitely say that an equilibrium solid state exists even in this case.

NUCLEAR STRUCTURE Neutron solidification, possibility of solidification of neutron star matter examined.

Simple relations for the excitation energies $E 2$ and the transition probabilities $B (E 2)$ of neighboring doubly even nuclides

R. Patnaik, R. Patra, and L. Satpathy

Phys. Rev. C 12, 2038 (1975) - Published 1 December, 1975

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For even-even nuclei, the excitation energy $E 2$ and the reduced transition probability $B (E 2)$ between the ground state and the first excited $2^{+}$ state have been considered. On the basis of different models, it is shown that for a nucleus [ $N$ , $Z$ ] the relations $E 2 [N, Z] + E 2 [N + 2, Z + 2] - E 2 [N + 2, Z] - E 2 [N, Z + 2] \approx 0$ and $B (E 2) [N, Z] + B (E 2) [N + 2, Z + 2] - B (E 2) [N + 2, Z] - B (E 2) [N, Z + 2] \approx 0$ hold good, except in certain specified regions. The validity of these difference equations is tested with the available experimental data. The difference equation of Ross and Bhaduri is shown to follow from our approach. Some predictions of unmeasured $E 2$ and $B (E 2)$ values have been made.

NUCLEAR STRUCTURE Simple relations for $E 2$ transition probabilities and excitation energies of first excited $2^{+}$ states in even-even nuclei.

Structure of ${}^{4}{He}$ and ${}^{12}C$ nuclei

Wahby Wadia and Samia Moharram

Phys. Rev. C 12, 2050 (1975) - Published 1 December, 1975

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A wave function which is an admixture of the ( $0 s$ ) and ( $1 s$ ) states is found to account for the diffraction minimum of the form factor of elastic electron scattering by ${}^{4}{He}$ . Brink's cluster model for ${}^{12}C$ has been investigated by means of a convenient expansion procedure. The model is found to be substantially different from the classical $α$ -particle model and to account satisfactorily for the high-energy electron scattering data. Further, the connection between Brink's model and the shell model has been established.

NUCLEAR STRUCTURE ${}^{4}{He}$ , ${}^{12}C$ model wave functions; comparison with electron scattering.

Unified weak-coupling model of mass 13 nuclei, including exchange effects

M. R. Meder and J. E. Purcell

Phys. Rev. C 12, 2056 (1975) - Published 1 December, 1975

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Structure calculations on ${}^{13}C$ and ${}^{13}N$ are reported which use the weak-coupling model as a starting point. The same model is used for both positive- and negative-parity states. Exchange effects, which are especially important in the negative-parity states, are included by perturbation theory. ${}^{12}C$ core states used are $0^{+}$ , $2^{+}$ , $0^{+ *}$ , $3^{-}$ , $4^{+}$ , and single-particle shell model states up through the $s - d$ shell (plus the $1 f_{\frac{7}{2}}$ , in one case) are included. Energy levels, moments, and transition rates are calculated and compared, where possible, with experiment. Generally, the results are excellent, except for $E 1$ rates. Effective charges are used in the electromagnetic rate results.

NUCLEAR STRUCTURE ${}^{13}C$ , ${}^{13}N$ . Calculated levels, moments, transition rates, $log (ft)$ ; negative and positive parity, exchange effects.

Interpretation of inversions of single-particle levels in self-consistent field theories

R. L. Becker and J. P. Svenne

Phys. Rev. C 12, 2067 (1975) - Published 1 December, 1975

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An interpretation is offered for the level inversion that usually occurs in self-consistent field calculations when only one of a pair of symmetry-related levels is occupied: the single-particle energy of the level unoccupied in the $A$ -particle system is its energy of removal from the ( $A + 1$ )-particle system. The correction of this energy to convert it to the corresponding energy in system $A$ is simply given. When both symmetry-related levels are calculated in the same system there is no level inversion. The prescription to occupy the lowest levels should be amended to state that the energies should all correspond to removal energies from system $A$ .

NUCLEAR STRUCTURE Self-consistent field theory (HF, RBHF); broken symmetry. Level inversion explained; oscillation of level occupancies with iteration avoided.

$N = Z$ even-even nuclei in the $2 s - 1 d$ shell

P. Mpanias and M. L. Rustgi

Phys. Rev. C 12, 2072 (1975) - Published 1 December, 1975

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The ground-state properties of $N = Z$ even-even $2 s - 1 d$ shell nuclei are studied within the framework of the Hartree-Fock approximation employing the modified Yale potential and the supersoft core potential. Shell-model spaces of various sizes are used. The results are compared with similar but less sophisticated calculations published earlier.

NUCLEAR STRUCTURE ${}^{16}O$ , ${}^{20}{Ne}$ , ${}^{24}{Mg}$ , ${}^{28}{Si}$ , ${}^{32}S$ , ${}^{36}A$ , ${}^{40}{Ca}$ ; Hartree-Fock method with various shell-model spaces. Modified Yale and supersoft core interactions.

New methods for solving the Bethe-Goldstone equation

M. Znojil

Phys. Rev. C 12, 2077 (1975) - Published 1 December, 1975

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Two methods of calculation of the Brueckner correlated wave function are suggested for the Bethe-Goldstone equation defined with the propagator $\frac{Q}{(ω + Q T Q)}$ . The first method generalizes the Goldhammer-Pintar approach and is applicable when the energy denominators of the reference and exact propagators are different. The difference is treated as a perturbation. The second method consists in a direct inclusion of a harmonic Pauli projector. The only approximation is an arbitrary energy cutoff $\tilde{N}$ in the oscillator basis. Equations to be solved are written for partial waves. They are integral equations similar to the Schrödinger equation plus a set of linear algebraic equations. They are solved for a separable potential and transformed into differential ones in the case of a local potential. The number of equations is given and the error is a priori estimated using qualitative arguments.

NUCLEAR STRUCTURE Two methods for solving Bethe-Goldstone equation suggested.

Lifetimes of some low-lying levels of ${}^{55}{Co}$

S. E. Caldwell, L. A. Alexander, R. G. Arns, B. J. Brunner, M. A. Kovash, C. M. Rozsa, and J. W. Smith

Phys. Rev. C 12, 2084 (1975) - Published 1 December, 1975

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Excitation energies and nuclear lifetimes of levels in ${}^{55}{Co}$ have been measured via the reactions ${}^{54}{Fe} ({}^{3}{He}, d γ) {}^{55}{Co}$ induced by 11.0 MeV incident ${}^{3}{He}^{+ +}$ particles. The Doppler shifted $γ$ -ray spectra, taken in coincidence with the outgoing deuterons, were fitted by a line shape analysis program to determine the lifetimes. Experimental results for excitation energies (±1 keV) and lifetimes (ps) are: 2166, ${0.141}_{- 0.021}^{+ 0.020}$ ; 2566, ${0.620}_{- 0.090}^{+ 0.120}$ ; 2940, ≥0.590; 3324, ${0.090}_{- 0.012}^{+ 0.017}$ ; 4166, ${0.050}_{- 0.005}^{+ 0.010}$ .

NUCLEAR STRUCTURE ${}^{54}{Fe} ({}^{3}{He}, d γ)$ , $E = 11$ MeV; measured $E_{γ}$ , Doppler shifts; ${}^{55}{Co}$ deduced levels, lifetimes.

Calculation of the mass parameter in the theory of self-cranked generator coordinates

L. Wilets, D. R. Tuerpe, and P. K. Haff

Phys. Rev. C 12, 2088 (1975) - Published 1 December, 1975

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The self-cranked generator coordinate (SCGC) method of Haff and Wilets, together with constrained Hartree-Fock-Bogoliubov wave functions, has been used to calculate the mass parameter $B_{Q}$ for quadrupole deformations. A simple ansatz reduces the required integrals to a form similar to that required in Hartree-Fock calculations, and the same matrix elements of the Hamiltonian occur in both cases. The results are sensitive to numerical approximations and care must be exercised to maintain accuracy. Since the SCGC method adds another variational function, the energy is lowered relative to the usual generator coordinate method, and hence $B_{Q}$ is increased. For a particular sample calculation, the correction more than doubled $B_{Q}$ .

NUCLEAR STRUCTURE Self-cranked generator coordinate method employed to calculate quadrupole mass parameter and potential energy. Constrained Hartree-Fock-Bogoliubov wave functions. ${}^{108}{Ru}$ .

Decay of ${}^{49}{Cr}$

S. V. Jackson, E. A. Henry, and R. A. Meyer

Phys. Rev. C 12, 2094 (1975) - Published 1 December, 1975

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For the decay of ${}^{49}{Cr}$ the intensities of the 1361-, 1423-, 1508-, 1514-, and 1570-keV $γ$ rays are found to be 0.85, 0.19, 0.15, 0.49, and 0.37, respectively, relative to $I_{γ} = 1000$ for the 90-keV $γ$ ray. Four other previously reported $γ$ rays are shown to be sum peaks or contaminants. The recalculated $β$ -decay branches and $log ft$ values (in parentheses) for ${}^{49}{Cr}$ decay are ground state (5.51), 90.639- (4.94), 152.928- (4.74), 1514.5- (5.71), 1661.1- (6.06), 2181.7- (7.0), 2236- (6.6), and 2310-keV (7.1). The known ${\frac{3}{2}}^{+}$ level at 748 keV was not observed to be populated and a limit of $log ft > 9$ was found for that level.

RADIOACTIVITY ${}^{49}{Cr}$ [from ${}^{50}{Cr} (n, 2 n)$ ]; measured $E γ$ , $I γ$ ; deduced $log ft$ , ${}^{49}V$ deduced levels. Enriched target, Ge(Li) detectors.

Comment on three-particle model of the $NN π$ system

Michael G. Fuda

Phys. Rev. C 12, 2097 (1975) - Published 1 December, 1975

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It is shown that the one pion exchange interaction that arises in the Afnan-Thomas model of the $NN π$ system has unphysical matrix elements which connect spin singlet and spin triplet states of the two nucleon system. The unphysical coupling arises only between singlet and triplet states for which the orbital angular momentum is equal to the total angular momentum. This coupling vanishes in the static limit.

NUCLEAR REACTIONS Use of Faddeev equations with separable interactions to describe $NN π$ system; nonrelativistic; difficulty with one pion exchange interaction.

RAPID COMMUNICATION

Constrained Hartree-Bogoliubov solutions as a basis for time-dependent calculations

G. Schütte and L. Wilets

Phys. Rev. C 12, 2100(R) (1975) - Published 1 December, 1975

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Starting from static constrained Hartree-Fock solutions, a numerically tractable method is proposed to study the inner excitation of a nucleus during collective deformations like fission. A prescription is proposed to determine the dynamics of one collective degree of freedom.

NUCLEAR REACTIONS Fission from saddle to scission, time-dependent equations, constrained Hartree-Bogoliubov solutions as basis. Trajectory for collective variable from energy conservation.

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Effective cross sections for the ( $n, 2 p n$ ), ( $n, 2 p$ ), and ( $n, 3 p n$ ) reactions using intermediate-energy neutrons

Calculation of the covariant pion-nucleus optical potential. I. Kinematical aspects

Longitudinal electron polarization for a second-forbidden beta decay

Gamma-ray angular distributions and parity tests in the decays of polarized ${}^{173}{Lu}$ and ${}^{174}{Lu}^{m, g}$

Two-particle, one-hole states in antimony nuclei and the decay of ${}^{121}{Te}^{m, g}$

Magnetic moment of the $I^{π} = {\frac{25}{2}}^{-}$ isomer in ${}^{179}{Hf}$ and anomalous orbital proton $g$ factor

Second class interactions and the electron-neutrino correlation in nuclear beta decay

Determination of the sign and magnitude of the nuclear quadrupole interaction by $β - γ$ directional correlations

Solidification of neutron matter

Simple relations for the excitation energies $E 2$ and the transition probabilities $B (E 2)$ of neighboring doubly even nuclides

Structure of ${}^{4}{He}$ and ${}^{12}C$ nuclei

Unified weak-coupling model of mass 13 nuclei, including exchange effects

Interpretation of inversions of single-particle levels in self-consistent field theories

$N = Z$ even-even nuclei in the $2 s - 1 d$ shell

New methods for solving the Bethe-Goldstone equation

Lifetimes of some low-lying levels of ${}^{55}{Co}$

Calculation of the mass parameter in the theory of self-cranked generator coordinates

Decay of ${}^{49}{Cr}$

Comment on three-particle model of the $NN π$ system

Constrained Hartree-Bogoliubov solutions as a basis for time-dependent calculations

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