Recent Articles

Integral form of energy matrix element

T. A. Antone

Phys. Rev. C 17, 1480 (1978) - Published 1 April, 1978

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The radial part of the matrix element of Goldhammer's Hamiltonian is expressed in the integral form. The variation principle is applied to give the maximum binding energy of the nuclear system. This results in a set of Morpurgo type coupled differential equations corresponding to each quantum of excitation.

NUCLEAR STRUCTURE A mathematical model for binding energy calculations.

Low excitation structure of ${}^{18}O$

I. Morrison, R. Smith, P. Nesci, and K. Amos

Phys. Rev. C 17, 1485 (1978) - Published 1 April, 1978

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The spectra of ${}^{18}O$ up to 6 MeV is explained in terms of the classic valence (two nucleons) plus four particle-two hole deformed state model but with a basis of the full $p$ and $s - d$ shells. Electromagnetic and nuclear ( $p p^{'}$ ) transition data are used to test the credibility of the associated wave functions.

NUCLEAR STRUCTURE ${}^{18}O$ , calculated $J^{π}$ transition rates, multideterminant projected Hartee-Fock method. Used in ( $p, p^{'}$ ) data analyses.

RAPID COMMUNICATION

Influence of Coulomb and nuclear forces on the pattern of the double differential cross section $\frac{d^{2} σ}{d θ dE}$ for deep inelastic reactions

M. Berlanger, P. Grange, H. Hofmann, C. Ngô, and J. Richert

Phys. Rev. C 17, 1495(R) (1978) - Published 1 April, 1978

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The tremendous change in the pattern of the Wilczynski curves for deep inelastic reactions with the product $Z_{1}$ $Z_{2}$ is interpreted within a model including both dissipation and statistical fluctuations. The competition between Coulomb and nuclear forces seems to account for this effect.

NUCLEAR REACTIONS Calculation of double differential cross sections $\frac{d^{2} σ}{d θ dE}$ for deep inelastic reactions.

RAPID COMMUNICATION

Radioactive decay of ${}^{139}{Ba}$

Robert E. Laird

Phys. Rev. C 17, 1498(R) (1978) - Published 1 April, 1978

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The decay of ${}^{139}{Ba}$ to levels of ${}^{139}{La}$ was studied to resolve discrepancies in previous determinations of the decay scheme of this isotope. The existence of 1257, 1601, 1691, 1762, and 1797 keV $γ$ rays has been confirmed and some new relative intensities established.

RADIOACTIVITY ${}^{139}{Ba}$ ; measured $E_{γ} : I_{γ}$ .

RAPID COMMUNICATION

Distorted-wave impulse-approximation evaluation of sum rule for hypernuclear formation in forward ( $K^{-}, π^{-}$ )

G. N. Epstein, F. Tabakin, C. M. Vincent, A. Gal, and L. S. Kisslinger

Phys. Rev. C 17, 1501(R) (1978) - Published 1 April, 1978

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The summed hypernuclear formation cross section at O° in ( $K^{-}, π^{-}$ ) reactions, for kaons of laboratory momentum $p_{K} = 900$ MeV/c, is evaluated within the distorted-wave impulse approximation using a non-energy-weighted sum rule obtained with the closure assumption. A detailed study of distortion effects results in agreement with eikonal estimates. Possible corrections to closure are mentioned. The final results are in strong disagreement with cross sections recently measured by Brückner et al.

NUCLEAR REACTIONS ( $K^{-}, π^{-}$ ); ${}^{12}C$ , ${}^{40}{Ca}$ targets; $K^{-}$ lab momentum 900 MeV/c; calculated $σ (0 °)$ using sum rule; realistic $K^{-}$ , $π^{-}$ distortions.

RAPID COMMUNICATION

Pole positions of ${}^{5}{He}$ resonances from various models of the $n - {}^{4}{He}$ interaction

M. U. Ahmed and P. E. Shanley

Phys. Rev. C 17, 1505(R) (1978) - Published 1 April, 1978

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RAPID COMMUNICATION

Decay of ${}^{234}{Th}$ to the ${}^{234}{Pa}$ isomers

Y. Y. Chu and G. Scharff-Goldhaber

Phys. Rev. C 17, 1507(R) (1978) - Published 1 April, 1978

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The low-energy portion of the photon spectrum for the $β$ decay of ${}^{234}{Th}$ has been investigated with a carefully calibrated Ge(Li) detection system because of the excessive photon intensity of the $M 1$ 73.7-keV transition reported previously. The new photon intensity obtained for this transition relative to other strong transitions is consistent with the most recent conversion electron measurements in the two-step ${}^{234}{Pa}^{m}$ isomeric transition. The upper energy limit of the unobserved $E 3$ isomeric transition is discussed in terms of total converion coefficients, hindrance factors, and the detection limit of the recent conversion electron measurements.

RADIOACTIVITY ${}^{234}{Th}$ chemically separated sample from ${}^{238}U$ . Measured $E_{γ}$ , $I_{γ}$ .

RAPID COMMUNICATION

Cumulative mass yields in the neutron-induced fission of ${}^{239}{Pu}$ at the resonance energy of 0.3 eV

T. Kaiser and H. R. von Gunten

Phys. Rev. C 17, 1510(R) (1978) - Published 1 April, 1978

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Radiochemical techniques were used to measure the mass distribution of products in the fission of ${}^{239}{Pu}$ induced by neutrons at the 0.3 eV resonance. Cd and Gd filters produced neutron spectra suitable for these measurements. The valley-to-peak ratio thus obtained is 0.65 of that in fission induced by thermal neutrons.

NUCLEAR REACTIONS, FISSION ${}^{239}{Pu} (n, f)$ , $E = 0.3$ eV; measured yields of Sr, Ag, and Cd isotopes.

RAPID COMMUNICATION

Distorted-wave Born-approximation description of the ${}^{4}{He} (p, d) {}^{3}{He}$ reaction at $E_{p} = 770$ MeV

E. Rost, J. R. Shepard, and D. A. Sparrow

Phys. Rev. C 17, 1513(R) (1978) - Published 1 April, 1978

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The exact finite-range, distorted-wave Born approximation was used to compute ${}^{4}{He} (p, d) {}^{3}{He}$ cross sections at $E_{p} = 770$ MeV. The transition form factor was tied to measured electron- ${}^{4}{He}$ scattering and the calculated cross sections were insensitive to uncertainties in the distorting potentials. The calculated angular distributions do not reproduce the data.

NUCLEAR REACTIONS Computed DWBA cross sections for ${}^{4}{He} (p, d) {}^{3}{He}$ , $E_{p} = 770$ MeV.

RAPID COMMUNICATION

Ferromagnetism of dense neutron matter

J. Dabrowski, W. Piechocki, J. Rożynek, and P. Haensel

Phys. Rev. C 17, 1516(R) (1978) - Published 1 April, 1978

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The possibility of a ferromagnetic transition in dense neutron matter is investigated using a simplified model of a pure hard core gas, with core radius $c$ . Previous estimates of the density at which the ferromagnetic transition would occur are shown to be incorrect. The inclusion of terms cubic in $k_{F} c$ , in particular the $P$ state interaction, leads to the conclusion that neutron matter in the liquid phase should not exhibit ferromagnetism.

NUCLEAR STRUCTURE Ferromagnetism of dense hard-core neutron and nuclear matter.

Erratum: Family of nuclear mass relations

J. E. Monahan and F. J. D. Serduke

Phys. Rev. C 17, 1519 (1978) - Published 1 April, 1978

Investigation of 54- to 99-MeV ${}^{6}{Li}$ -induced reactions on rare earth targets

J. G. Fleissner, D. A. Rakel, F. P. Venezia, E. G. Funk, J. W. Mihelich, and H. A. Smith, Jr.

Phys. Rev. C 17, 1001 (1978) - Published 1 March, 1978

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Cross section measurements for the reactions ${}^{150}{Sm}$ and ${}^{142, 146, 150}{Nd} ({}^{6}{Li}, x n + y p)$ have been performed in the 50-100-MeV energy range. The experimental excitation functions have been compared to the predictions of the geometry dependent hybrid model. Reasonable agreement between theory and experiment is achieved for the ( $xn$ ) exit channels while significant differences exist for charged particle exit channels. These differences can be attributed to a contribution from breakup of the ${}^{6}{Li}$ projectile with reactions being induced by the breakup fragments.

NUCLEAR REACTIONS ${}^{150}{Sm}$ , ${}^{142, 146, 150}{Nd} ({}^{6}{Li}, x n y p γ)$ , enriched targets, $E = 54 - 99$ MeV; measured in-beam, decay $γ$ rays. Deduced Eu, Sm isotopic yields. Geometry-dependent hybrid model; breakup of ${}^{6}{Li}$ .

Yrast decay schemes from heavy-ion + ${}^{48}{Ca}$ fusion-evaporation reactions. III. ${}^{57, 58}{Fe}$ , ${}^{54, 55}{Cr}$ , and ${}^{57, 58}{Mn}$

A. M. Nathan, J. W. Olness, E. K. Warburton, and J. B. McGrory

Phys. Rev. C 17, 1008 (1978) - Published 1 March, 1978

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Fusion-evaporation reactions induced by beams of 25-65 MeV ${}^{13}C$ , ${}^{15}N$ , ${}^{11}B$ , and ${}^{9}{Be}$ on an isotopically enriched ${}^{48}{Ca}$ target have been used to populate high-spin yrast levels in ${}^{57, 58}{Fe}$ , ${}^{54, 55}{Cr}$ , and ${}^{57, 58}{Mn}$ . Measurements consisted of $γ$ -ray excitation functions, angular distributions, $γ - γ$ coincidences, and recoildistance and Doppler shift lifetime measurements, from which were deduced the energy levels, $γ$ -ray branching ratios, most probable spin-parity assignments, and level lifetimes. Comparision is made with a large-basis shell-model calculation.

NUCLEAR REACTIONS ${}^{48}{Ca} ({}^{13}C, x n, y p, z α) {}^{57, 58}{Fe}$ , ${}^{54, 55}{Cr}$ , and ${}^{57, 58}{Mn}$ ; ${}^{48}{Ca} ({}^{15}N, α 2 n) {}^{57}{Mn}$ ; ${}^{48}{Ca} ({}^{11}B, p x n) {}^{54, 55}{Cr}$ ; and ${}^{48}{Ca} ({}^{9}{Be}, 3 n) {}^{54}{Cr}$ . $E = 25 - 65$ MeV; measured $σ (E, E_{γ})$ and coin; deduced levels; measured $σ (E_{γ}, θ)$ ; deduced $J^{π}$ for highspin levels; measured RDM and Doppler shifts; deduced $t_{m}$ , ${| M (M 1) |}^{2}$ , and ${| M (E 2) |}^{2}$ . Enriched targets, Ge(Li) detectors.

Recoil-distance measurement of lifetimes of rotational states in ${}^{164}{Dy}$

R. O. Sayer, E. Eichler, N. C. Singhal, R. Sturm, N. R. Johnson, and M. W. Guidry

Phys. Rev. C 17, 1026 (1978) - Published 1 March, 1978

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Lifetimes of the $4^{+}$ to $12^{+}$ levels in the ground state rotational band of ${}^{164}{Dy}$ have been measured by means of the Doppler-shift recoil-distance technique. Our best values for the mean lives of the $4^{+}$ - $12^{+}$ states are 286 ± 15, 39.0 ± 1.9, 10.4 ± 0.7, 3.7 ± 0.8, and 1.6 ± 0.8 ps, respectively. The corresponding $B (E 2)$ values exhibit a spin dependence consistent with rigid-rotor predictions. Within the respective experimental uncertainties, previous results obtained by multiple Coulomb excitation and Doppler-broadened line shape methods are in agreement with the present recoil-distance values.

NUCLEAR REACTIONS ${}^{164}{Dy}$ ( ${}^{40}{Ar}$ , ${}^{40}{Ar'}$ ), $E = 152.6$ MeV; measured $τ$ , $E_{γ}$ ; deduced $B (E 2)$ .

Isospin forbidden and allowed reactions ${}^{16}O (α, α_{0}) {}^{16}O$ and ${}^{16}O (α, γ) {}^{20}{Ne}$

D. J. Steck

Phys. Rev. C 17, 1034 (1978) - Published 1 March, 1978

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Six ${}^{20}{Ne}$ levels have been investigated in detail via the ${}^{16}O + α$ channel between $6.9 \leq E_{α} \leq 10.2$ MeV. Level parameters for states at $E_{x} ({}^{20}{Ne}) = 10.264 \pm 0.008, 11.077 \pm 0.008, 11.259 \pm 0.008, 11.552 \pm 0.008, 12.237 \pm 0.008, and 12.390 \pm 0.008$ MeV have been extracted from $γ$ decay properties and phase shift analysis of the elastic scattering. With the exception of the 11.552 and 12.39 MeV states, these levels display primarily $T = 1$ characteristics. In addition to some previously reported $T = 0$ states, several other weak $γ$ decaying resonances were observed at 11.97 ± 0.04, 12.05 ± 0.04, and 12.49 ± 0.02 MeV but were not studied in detail. Charge dependent matrix elements (4-120 keV) for isospin mixing of $T = 1$ states with nearby $T = 0$ states were estimated from the measured level parameters.

NUCLEAR REACTIONS ${}^{16}O (α, α_{0}) {}^{16}O$ , ${}^{16}O (α, γ_{0, 1, 2}) {}^{20}{Ne}$ , ${}^{16}O (α, α_{2} γ_{6.13}) {}^{16}O$ , $E_{α} = 6.9 - 10.2$ MeV; measured $σ (E, θ)$ . Deduced ${}^{20}{Ne}$ level parameters, $J$ , $π$ , $T$ , $γ$ -branching ratios, $Γ_{γ}$ , $Γ$ , $E_{R}$ . Isospin mixing, charge dependent Hamiltonian, IAS.

Explosive nucleosynthesis, equilibrium thermodynamics, and relativistic heavy-ion collisions

A. Z. Mekjian

Phys. Rev. C 17, 1051 (1978) - Published 1 March, 1978

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A description of the formation of composite nuclei observed in relativistic heavy-ion collisions is developed. The description is analogous to that used in accounting for the formation of nuclei under explosive conditions, as encountered in the expansion of an isotropic and homogeneous universe and in imploding-exploding supermassive stars. The model studied is one in which composite nuclei are formed in the space-time evolution of a rapidly expanding system of nucleons. Within the framework of this model, it is shown that reaction rates may initially be fast compared to expansion time scales, that detailed balance can then be met and a quasiequilibrium established for a short period of time and limited volume of space in this space-time evolution. An idealized equilibrium model is then proposed which contains a sharp cutoff from equilibrium to free expansion. In such a model the observed properties of the composite particles reflect a "frozen in" equilibrium state. A simple discussion is then presented showing that the volume at which the transition occurs is related to the finite size of the correlated structures in the system. A key result in the approach developed is that properties of the composite particle cross sections can be used to obtain information on the size of the emitting region without resorting to a Hanbury-Brown-Twiss correlation measurement. Another important result is that cross sections for composite nuclei are characterized by Maxwell-Boltzmann distributions in some rest system and recent data will be discussed from this viewpoint. The thermodynamic properties of the system, such as the equation of state and the energy-temperature relationship are investigated. The effect of continuum correlations from resonances and echoes will also be discussed.

NUCLEAR REACTIONS Thermodynamic model of heavy-ion collisions at relativistic energies. Theory of formation of composite nuclei in space-time evolution of an expanding system of nucleons.

Recoil range distributions of heavy mass products in deep inelastic reactions with gold and uranium targets

R. J. Otto, G. T. Seaborg, and M. M. Fowler

Phys. Rev. C 17, 1071 (1978) - Published 1 March, 1978

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Recoil range distributions have been measured for the elements between lutetium ( $Z = 71$ ) and astatine ( $Z = 85$ ) produced in heavy ion reactions of 420, 491, and 581 MeV ${}^{86}{Kr}$ with ${}^{197}{Au}$ , 686 MeV ${}^{86}{Kr}$ with ${}^{238}U$ , and 868 MeV ${}^{136}{Xe}$ with ${}^{197}{Au}$ ; the relative yields were established by use of x-ray spectrometry. These elements have been identified in radioanalytical mass distribution studies and kinematic studies as deep inelastic and quasielastic transfer reaction products. For the uranium target reactions they form the mass distribution colloquially referred to as the "gold finger." The measured recoil range distributions for the gold target reactions are correlated with energy and angular distribution measurements made on the projectile - like fragments formed in deep inelastic reactions.

NUCLEAR REACTIONS ${}^{197}{Au} (Kr, X) Y$ , $E_{lab} = 420, 491, 581$ MeV; ${}^{197}{Au} ({}^{136}{Xe}, X) Y$ , $E_{lab} = 868$ MeV; ${}^{238}U ({}^{86}{Kr}, X) Y$ , $E_{lab} = 686$ MeV. Measured recoil range distributions for $72 <~ Z_{y} <~ 84$ .

Subthreshold photofission of ${}^{235}U$ and ${}^{232}{Th}$

C. D. Bowman, I. G. Schröder, K. C. Duvall, and C. E. Dick

Phys. Rev. C 17, 1086 (1978) - Published 1 March, 1978

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Photofission cross sections for ${}^{232}{Th}$ , and ${}^{236}U$ have been measured in the energy range from 3.25 to 5.75 MeV and for ${}^{234}U$ and ${}^{236}U$ at 3.5 MeV. The cross sections change by over seven orders of magnitude for this energy range. Cross section shapes are significantly different for different isotopes indicating a strong sensitivity to fission barrier parameters.

NUCLEAR REACTIONS, FISSION Barrier shape; fission; nuclear reactions; photofission bremsstrahlung; threshold; tract counting.

Fission product yeilds from 6-9 MeV neutron-induced fission of ${}^{235}U$ and ${}^{238}U$

T. C. Chapman, G. A. Anzelon, G. C. Spitale, and D. R. Nethaway

Phys. Rev. C 17, 1089 (1978) - Published 1 March, 1978

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The yields of 28 mass chains have been measured for fission of ${}^{235}U$ and ${}^{238}U$ induced by neutrons at four different energies from 6.0 to 9.1 MeV. This is the first experimental measurement where sufficient energy resolution was obtained to observe the effect of the onset of second chance fission in the case of symmetric fission. The ${}^{111}{Ag}$ and ${}^{112}{Pd}$ results are compared with measurements at other neutron energies and with previous theoretical predictions. All nuclide results are presented in tabular form, as a function of neutron energy. The mass chains measured range from 84 to 156.

NUCLEAR REACTIONS, FISSION ${}^{235}U (n, f)$ and ${}^{238}U (n, f)$ , $E = 6.0, 7.1, 8.1, 9.1$ MeV; measured yields of 28 mass chains.

MILESTONE

Dynamics of induced fission

J. W. Negele, S. E. Koonin, P. Möller, J. R. Nix, and A. J. Sierk

Phys. Rev. C 17, 1098 (1978) - Published 1 March, 1978

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Induced fission of ${}^{236}U$ is calculated in the time-dependent mean-field approximation assuming axial and reflection symmetry and omitting the spin-orbit interaction. Constrained static solutions are used to generate the appropriate initial condition and are compared in detail with results of macroscopic-microscopic calculations. Although dynamic mean-field results are strongly dependent upon an effective pairing gap, predicted observables are consistent with experiment for plausible values of the gap. Detailed comparisons with macroscopic models indicate that both a modified one-body dissipation and two-body viscosity yield observables similar to those of the mean-field theory, even though these physical dissipation mechanisms are fundamentally different.

NUCLEAR REACTIONS, FISSION ${}^{236}U$ induced fission calculated in time-dependent mean-field approximation and with modified liquid-drop model. Comparison of dissipation mechanisms.

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Integral form of energy matrix element

Low excitation structure of ${}^{18}O$

Influence of Coulomb and nuclear forces on the pattern of the double differential cross section $\frac{d^{2} σ}{d θ dE}$ for deep inelastic reactions

Radioactive decay of ${}^{139}{Ba}$

Distorted-wave impulse-approximation evaluation of sum rule for hypernuclear formation in forward ( $K^{-}, π^{-}$ )

Pole positions of ${}^{5}{He}$ resonances from various models of the $n - {}^{4}{He}$ interaction

Decay of ${}^{234}{Th}$ to the ${}^{234}{Pa}$ isomers

Cumulative mass yields in the neutron-induced fission of ${}^{239}{Pu}$ at the resonance energy of 0.3 eV

Distorted-wave Born-approximation description of the ${}^{4}{He} (p, d) {}^{3}{He}$ reaction at $E_{p} = 770$ MeV

Ferromagnetism of dense neutron matter

Erratum: Family of nuclear mass relations

Investigation of 54- to 99-MeV ${}^{6}{Li}$ -induced reactions on rare earth targets

Yrast decay schemes from heavy-ion + ${}^{48}{Ca}$ fusion-evaporation reactions. III. ${}^{57, 58}{Fe}$ , ${}^{54, 55}{Cr}$ , and ${}^{57, 58}{Mn}$

Recoil-distance measurement of lifetimes of rotational states in ${}^{164}{Dy}$

Isospin forbidden and allowed reactions ${}^{16}O (α, α_{0}) {}^{16}O$ and ${}^{16}O (α, γ) {}^{20}{Ne}$

Explosive nucleosynthesis, equilibrium thermodynamics, and relativistic heavy-ion collisions

Recoil range distributions of heavy mass products in deep inelastic reactions with gold and uranium targets

Subthreshold photofission of ${}^{235}U$ and ${}^{232}{Th}$

Fission product yeilds from 6-9 MeV neutron-induced fission of ${}^{235}U$ and ${}^{238}U$

Dynamics of induced fission

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