Recent Articles

Fission of odd- $A$ and doubly odd actinide nuclei induced by direct reactions

B. B. Back, H. C. Britt, Ole Hansen, B. Leroux, and J. D. Garrett

Phys. Rev. C 10, 1948 (1974) - Published 1 November, 1974

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Fission probability distributions have been measured using ( $d, p f$ ), ( $t, p f$ ), ( ${}^{3}{He}, d f$ ), ( ${}^{3}{He}, α f$ ), and ( $t, α f$ ) reactions to excite a variety of odd- $A$ and odd-odd actinide nuclei. Fission of the residual nuclei ${}^{229, 231}{Th}$ , ${}^{231, 232, 233}{Pa}$ , ${}^{234, 235, 236, 237, 238, 239}{Np}$ , ${}^{241}{Pu}$ , ${}^{240, 241, 243, 245, 247}{Am}$ , ${}^{249}{Cm}$ , and ${}^{249}{Bk}$ was studied. These results and other data available from previous ( $d, p f$ ), ( $t, p f$ ), and ( $n, f$ ) studies are analyzed with a statistical model to obtain estimates of the heights and curvatures of one or both peaks of the double humped fission barrier. Estimates of barrier parameters are obtained for the above nuclei and for ${}^{233}{Th}$ , ${}^{235, 237, 239}U$ , ${}^{239, 243, 245}{Pu}$ , ${}^{242, 244}{Am}$ , ${}^{245, 247}{Cm}$ , and ${}^{253}{Cf}$ . Systematic variations of the barrier parameters are discussed.

NUCLEAR REACTIONS, FISSION Measured fission probabilities, $E^{*} \leq 7.5$ MeV for ${}^{229, 231}{Th}$ , ${}^{231, 232, 233}{Pa}$ , ${}^{234, 235, 236, 237, 238, 239}{Np}$ , ${}^{241}{Pu}$ , ${}^{240, 241, 243, 245, 247}{Am}$ , ${}^{249}{Cm}$ , and ${}^{249}{Bk}$ using ( $d, p f$ ), ( $t, p f$ ), ( ${}^{3}{He}, d f$ ), ( ${}^{3}{He}, α f$ ), and ( $t, α f$ ) reactions. Deduced properties of the double peaked fission barrier for these nuclei and for ${}^{233}{Th}$ , ${}^{235, 237, 239}U$ , ${}^{239, 243, 245}{Pu}$ , ${}^{242, 244}{Am}$ , ${}^{245, 247}{Cm}$ , and ${}^{253}{Cf}$ .

Levels in ${}^{158}{Gd}$ populated in the decay of 46-min ${}^{158}{Eu}$

A. F. Kluk, Noah R. Johnson, and J. H. Hamilton

Phys. Rev. C 10, 1966 (1974) - Published 1 November, 1974

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The series of investigations of level properties in even gadolinium nuclei has been extended to ${}^{158}{Gd}$ . $γ$ rays emitted in the radioactive decay of ${}^{158}{Eu}$ were studied with large volume Ge(Li) detectors in both singles and coincidence modes to reveal a total of 132 transitions, 94 of which were incorporated in a level scheme involving 31 excited states. Several of the level assignments clarified conflicting data in the literature and 12 of the levels had not been observed previously. The coincidence measurements have provided reliable branching ratios for members of the $γ$ -vibrational band and members of $K = 0^{-} and 1^{-}$ octupole bands. Analyses of the data for the octupole bands are compared with theory. In ${}^{154}{Gd}$ and ${}^{156}{Gd}$ the $K = 0^{-}$ octupole band lies lower than the $K = 1^{-}$ band, in agreement with theoretical expectations that the $K = 0^{-}$ component of the $λ = 3$ vibration is the most collective. However, in ${}^{158}{Gd}$ this trend is reversed and the $K = 1^{-}$ component is lowest.

RADIOACTIVITY ${}^{158}{Eu}$ [from ${}^{160}{Gd} (d, α)$ ]; measured $E_{γ}$ , $I_{γ}$ , $γ - γ$ coin; deduced $log ft$ . ${}^{158}{Gd}$ deduced levels, $J$ , $π$ . Enriched target, Ge(Li) detectors.

Decay of the $K^{π} = 8^{-}$ isomer in ${}^{182}{Hf}$

T. E. Ward, P. E. Haustein, J. B. Cumming, and Y. Y. Chu

Phys. Rev. C 10, 1983 (1974) - Published 1 November, 1974

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The decay of 61.5-min ${}^{182}{Hf}^{m} (K^{π} = 8^{-})$ in chemically separated and mass-separated sources has been studied by means of Ge(Li) detectors and a plastic scintillation detector. Twenty-eight $γ$ rays, and two $β$ rays of 480±50 and 970±70 keV, were assigned to the decay of ${}^{182}{Hf}^{m}$ . The 480-keV $β$ group was observed to be in coincidence with high-energy $γ$ rays. Ge(Li)-Ge(Li) $γ - γ$ coincidence measurements established the $K^{π} = 0^{+}$ ground state rotational band of ${}^{182}{Hf}$ up to the $I = 8$ member. The energy of the isomeric state is at 1172.9 keV in ${}^{182}{Hf}$ . ${}^{182}{Hf}^{m}$ decays 54% by negatron emission to levels at 653, 1116, and 1337 keV in ${}^{182}{Ta}$ . The 653- and 1116-keV levels are identified as $K^{π} = 9^{-} and 7^{-}$ states, respectively, with possible Nilsson configurations of ${\frac{9}{2}}^{-} {[514]}_{p}$ , ${\frac{9}{2}}^{+} {[624]}_{n}$ , and ${\frac{7}{2}}^{+} {[404]}_{p}$ , ${\frac{7}{2}}^{-} {[514]}_{n}$ . The $Q$ value for $β$ decay of ${}^{182}{Hf}$ has been inferred to be 432±41 keV.

RADIOACTIVITY ${}^{182}{Hf}^{m}$ ; measured $T_{\frac{1}{2}}$ , $E_{γ}$ , $I_{γ}$ , $E_{β}$ , $γ γ$ coinc, $γ β$ coinc. ${}^{182}{Hf}$ deduced levels, $J$ , $π$ , $Q$ . ${}^{182}{Ta}$ deduced levels, $J$ , $π$ .

Half-lives of ${}^{6}{He}$ , ${}^{19}{Ne}$ , and ${}^{42}{Sc}^{m}$

D. H. Wilkinson and D. E. Alburger

Phys. Rev. C 10, 1993 (1974) - Published 1 November, 1974

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The half-lives of ${}^{6}{He}$ , ${}^{19}{Ne}$ , and ${}^{42}{Sc}^{m}$ have been measured as 808.1 ± 2.0 msec, 17.36 ± 0.06 sec, and 62.0 ± 0.3 sec, respectively. The activities were formed in the ${}^{9}{Be} (n, α) {}^{6}{He}$ , ${}^{19}F (p, n) {}^{19}{Ne}$ , and ${}^{42}{Ca} (p, n) {}^{42}{Sc}$ reactions. Half-lives of ${}^{6}{He}$ and ${}^{19}{Ne}$ were determined by multiscaling $β$ rays detected in a plastic scintillator, whereas the ${}^{42}{Sc}^{m}$ half-life was obtained from the decay of the $γ$ -ray spectrum in a Ge(Li) detector. The $ft$ values deduced for ${}^{6}{He}$ , ${}^{19}{Ne}$ , and ${}^{42}{Sc}^{m}$ are, respectively, 815.7 ± 4.2 sec, 1728.4 ± 6.7 sec, and 14 758 ± 91 sec. The values $| 〈 σ 〉 |$ of the Gamow-Teller matrix elements are given by, respectively, $R_{e} | 〈 σ 〉 | = 2.7472 \pm 0.0077, 1.6006 \pm 0.0042, and 0.6448 \pm 0.0021$ , where $R_{e}$ is the magnitude of the ratio of the axial to vector coupling constants appropriate for the respective complex nuclei.

RADIOACTIVITY ${}^{6}{He}$ , ${}^{19}{Ne}$ , ${}^{42}{Sc}^{m}$ : measured $T_{\frac{1}{2}}$ ; deduced $ft$ values and GT matrix elements.

Electric monopole transitions between $0^{+}$ states in ${}^{100}{Ru}$

Masahiro Koike, Hirokane Kawakami, Kazuhisa Komura, and Hironari Yamada

Phys. Rev. C 10, 1996 (1974) - Published 1 November, 1974

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The electric monopole ( $E 0$ ) transitions from the first and second excited $0^{+}$ states at 1130.3 and 1740.7 keV, respectively, in ${}^{100}{Ru}$ have been observed from the internal-conversion-electron studies of the decay of ${}^{100}{Rh}$ . The monopole strength for the first excited $0^{+}$ state $ρ (E 0; 0_{1}^{+} - 0_{g}^{+}) < 0.11$ is deduced as an upper limit. The dimensionless ratios of the reduced $E 0$ - to $E 2$ -transition probabilities $X$ are deduced: $X (\frac{E 0; 0_{1}^{+} - 0_{g}^{+}}{E 2; 0_{1}^{+} - 2_{1}^{+}}) = 0.011 \pm 0.001,$ $X (\frac{E 0; 0_{2}^{+} - 0_{g}^{+}}{E 2; 0_{2}^{+} - 2_{1}^{+}}) = 0.6 \pm 0.3$ . The observed branching ratio of the monopole strength for the second excited $0^{+}$ state is $\frac{ρ (0_{2}^{+} - 0_{g}^{+})}{ρ (0_{2}^{+} - 0_{1}^{+})} = 0.73 \pm 0.07$ . The experimental results are compared with the theory on the basis of the collective vibrations of an axially and nonaxially deformed nucleus.

RADIOACTIVITY ${}^{100}{Pd}$ [from ${}^{103}{Rh} (p, 4 n)$ ]; measured $E_{ce}$ , $I_{ce}$ , $E_{γ}$ , $I_{γ}$ , $γ - γ$ coin ${}^{100}{Ru}$ deduced ICC, $B (E 0)$ , branching ratio $\frac{B (E 0)}{B (E 2)}$ .

Coupled-channel calculations of electron scattering by samarium

R. L. Mercer and D. G. Ravenhall

Phys. Rev. C 10, 2002 (1974) - Published 1 November, 1974

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The coupled-channel method is considered in the context of relativistic hadron or lepton scattering by nonspherical dynamical nuclei. The program Zenith, which calculates electron-nucleus scattering via Coulomb and magnetic multipole potentials, is described and is applied in particular to the deformed samarium isotopes ${}^{152}{Sm}$ and ${}^{154}{Sm}$ . Two- and three-level calculations for the ground state 0+ and the excited states 2+ and 4+ containing all relevant $l = 0, 2, and 4$ Coulomb potentials are described. The elastic dispersion effect, arising mainly from coupling with the 2+ first excited state, and the dispersive effect on the 0+ → 2+ inelastic cross section, coming mainly from the diagonal $l = 2$ scattering in the excited state, are appreciable at 105 MeV, the highest energy at which measurements have been made. The largest effect, however, is that on the 0+ → 4+ inelastic cross section arising from the sequential excitation 0+ → 2+ → 4+ via the $l = 2$ potential. It has interesting small-angle behavior and becomes greater than 20% at the largest measured angles at 105 MeV. The dependence of some of these effects on energy and $q_{eff}$ is explored up to 250 MeV and 2 ${fm}^{- 1}$ .

NUCLEAR REACTIONS ${}^{152, 4}{Sm} (e, e^{'})$ calculations, coupled channels, $50 MeV < E < 250 MeV$ . Dispersive effects on elastic and inelastic cross sections.

Decay of ${}^{173}{Hf}$ and measurement of the half-life of the 128.3-keV state in ${}^{173}{Lu}$

E. G. Funk, D. R. Zolnowski, M. C. Madden, R. A. Belt, and J. W. Mihelich

Phys. Rev. C 10, 2015 (1974) - Published 1 November, 1974

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The $γ$ -ray and internal-conversion-electron spectra associated with the decay of ${}^{173}{Hf}$ (23.9 h) to ${}^{173}{Lu}$ have been studied using Ge(Li) and Si(Li) detectors. Approximately 70 transitions have been assigned to the ${}^{173}{Hf}$ decay and conversion coefficients and multipolarities have been obtained for 35 transitions. The results of $γ - γ$ coincidence measurements confirmed the placement of many transitions previously proposed by other investigators and were utilized in the construction of a decay scheme including about 50 transitions and several newly proposed levels. The existence of at least three transitions with significant $E 0$ content has been established. These depopulate states in two $K^{π} = {\frac{1}{2}}^{+}$ bands based at 981.7 and 1246.3 keV which are probably octupole-vibrational and $β$ -vibrational bands, respectively. $γ$ -ray branching ratio data are presented, and Nilsson state assignments and possible vibrational-state assignments are discussed. The half-life of the 128.3-keV ( ${\frac{1}{2}}^{-}$ ) state in the ${\frac{1}{2}}^{-} [541]$ band has been measured as 5.2 ± 0.5 nsec, and the $B (E 2)$ value for the enhanced 4.8-keV rotational transition depopulating the 128.3-keV state has been deduced using theoretical predictions for the internal-conversion coefficient.

RADIOACTIVITY ${}^{173}{Hf}$ [from ${}^{172}{Yb} (α, 3 n)$ ]; measured $E_{γ}$ , $I_{γ}$ , $I_{ce}$ , $t_{\frac{1}{2 γ}}$ $γ - γ$ coin; deduced $log ft$ . ${}^{173}{Lu}$ deduced levels, $J$ , $π$ , ICC. Enriched target; Ge(Li), Si(Li) detectors.

Nuclear muon-capture sum rules and mean nuclear excitation energies

B. Goulard and H. Primakoff

Phys. Rev. C 10, 2034 (1974) - Published 1 November, 1974

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A discussion is given of non-energy-weighted and of energy-weighted sum rules in nuclear muon capture. It is argued that the mean nuclear excitation energy in muon capture does not vary appreciably as $A$ and $Z$ vary. A combined non-energy-weighted and energy-weighted sum rule which constitutes a three-parameter fit to the experimental data on total muon-capture rates is presented.

Nonassociative algebra in nuclear boson-expansion theory

Susumu Okubo

Phys. Rev. C 10, 2045 (1974) - Published 1 November, 1974

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General boson expansion theory and Lie algebras $B_{n}$ and $D_{n}$

Susumu Okubo

Phys. Rev. C 10, 2048 (1974) - Published 1 November, 1974

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A general boson expansion theory for even and odd fermion states has been developed in both Dyson and unitary representations. We can construct them in several different forms, one of which essentially reproduces the formula of Marshalek. The underlying algebra may or may not obey the associative law. A connection of the theory with the Lie algebras $B_{n}$ and $D_{n}$ has been investigated. As a byproduct, construction of fermion annihilation and creation operators solely in terms of boson operators has been found.

Effect of curvature on nuclear surface energy

C. D. Bennett and D. G. Ravenhall

Phys. Rev. C 10, 2058 (1974) - Published 1 November, 1974

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For nuclear matter described by the Skyrme Hamiltonian, treated in the Thomas-Fermi one-fluid approximation, an examination is made of the dependence on curvature of the nuclear surface energy and the surface-tension pressure. These quantities are related in a manner which depends on the definition of the surface position. This question is explored both analytically and numerically for the first four terms in the expansion in powers of the curvature. The second-order term in the expansion which depends on the difference of the principal curvatures is also evaluated. The contribution of these effects in the nuclear mass formula is discussed briefly.

NUCLEAR STRUCTURE Thomas-Fermi model of curved surface, Skyrme interaction. Surface position, energy expansion in powers of curvature, contribution to mass formula.

Three - body force in the triton

Shin-Nan Yang

Phys. Rev. C 10, 2067 (1974) - Published 1 November, 1974

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We have derived a two-pion-exchange three-body potential by using a chiral-invariant Lagrangian for the pion-nucleon interaction. Only the three dominant lowest-order processes which give rise to a three-body interaction are included: (a) The second pion is emitted before the first pion is absorbed and the nucleon which emits the second pion goes into a positive-energy state; (b) one nucleon exchanges a $ρ$ meson with a pion; (c) one nucleon is scattered into an $N^{*} (1236)$ . We then proceed to evaluate the contribution of this three-body potential to the binding energy of the triton using a variational triton wave function. It is found that the two-pion-exchange three-body potential gives a significant contribution (2.32 MeV) to the binding energy of a triton.

NUCLEAR STRUCTURE ${}^{3}{He}$ , ${}^{3}H$ ; calculated contribution of three-body force to binding energy.

Brueckner-Hartree-Fock calculations and their density dependence

Ram K. Tripathi, Amand Faessler, and H. Müther

Phys. Rev. C 10, 2080 (1974) - Published 1 November, 1974

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Brueckner-Hartree-Fock (BHF) calculations are presented taking into account the Pauli operator in the self-consistent basis rather than in the oscillator basis. The definition of the single particle energies includes an on-shell rearrangement diagram (starting energy rearrangement) stemming from the only partial occupation of the occupied states due to the short range correlations. Further, it includes an off-shell diagram (Pauli rearrangement) term which originates from the density dependence of the Pauli operator. The three additional terms, the correction for the self-consistent Pauli operator, the starting energy, and the Pauli rearrangement terms, contribute significantly to the nucleus. It is shown that the definition of the single particle energies is analogous to that in density dependent Hartree-Fock calculations. One obtains all the effects of a density dependent force within the BHF formalism without making a detour to nuclear matter and thus avoids many of the approximations used in the calculations with density dependent forces. The method is applied here for ${}^{16}O$ using the Reid soft core and the Yale potential.

NUCLEAR STRUCTURE Brueckner-Hartree-Fock calculation in finite nuclei, ${}^{16}O$ calculated binding energy, rms radius, charge distribution, electron scattering.

Radius of the neutron distribution in ${}^{208}{Pb}$ from the ( $p, n$ ) quasielastic reaction

E. Friedman

Phys. Rev. C 10, 2089 (1974) - Published 1 November, 1974

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A microscopic analysis of the ${}^{208}{Pb} (p, n) {}^{208}{Bi}$ isobaric analog state (IAS) reaction is presented where the nucleon-nucleon interaction can be density dependent and the form factor for the reaction may have an imaginary term. The various ambiguities make it very difficult to obtain from this reaction accurate values for the radii of neutron distributions. Comparisons are also made with other results relating to the neutron distribution in ${}^{208}{Pb}$ .

NUCLEAR STRUCTURE ${}^{208}{Pb} (p, n)$ (IAS) DWBA calculations with density-dependent complex interactions; relation to neutron distributions.

Contributions of nucleon momenta to the pion optical potential

F. Cannata, C. W. Lucas, Jr., and C. Werntz

Phys. Rev. C 10, 2093 (1974) - Published 1 November, 1974

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The pion-nucleus scattering amplitude in the impulse approximation is expressed in terms of the invariant matrix for pion-nucleon scattering. It is pointed out that the linear nucleon momentum terms evaluated in the nuclear ground state constitute a longitudinal current that is nonzero. It is shown that these terms reduce by a factor of $\frac{1}{2}$ the $Δ^{2} ρ (\vec{r})$ addition to the optical potential obtained by Kisslinger and Tabakin.

NUCLEAR REACTIONS Calculated $σ (θ)$ for ${}^{12}C (π, π)$ . Relativistic effects in the optical potential.

RAPID COMMUNICATION

$K$ matrix and unitarity constraints on off-shell $T$ matrix elements

D. J. Kouri and F. S. Levin

Phys. Rev. C 10, 2096(R) (1974) - Published 1 November, 1974

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A discussion of off-shell properties of the $T$ matrix is given based on the damping equation and unitarity. The off-shell function $ϕ_{l} (k, q)$ of Baranger et al. is shown to be $ϕ_{l} (k, q) = cos δ_{l} (k) 〈 k | K_{l} (k^{2}) | q 〉$ , where $δ_{l}$ and $K_{l}$ are the phase shift and partial-wave $K$ (reaction) operator. The ratio of the imaginary to the real part of the half-off-shell partial-wave $T$ matrix elements is shown to be $tan δ_{l} (k)$ , thus providing a unitarity constraint to be satisfied by any approximate $T$ matrix elements. In addition, the imaginary part of the fully-off-shell $T$ matrix element is shown to be proportional to the product $ϕ_{l} (p, k) ϕ_{l} (k, q)$ . These results hold for both one-body and two-channel identical particle scattering.

RAPID COMMUNICATION

Weak parity-nonconserving potentials and circular polarization of $n - p$ capture gamma rays

M. L. Rustgi and H. J. Pirner

Phys. Rev. C 10, 2099(R) (1974) - Published 1 November, 1974

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Employing different models of the weak parity-violating vector-meson exchange potentials and three versions of the parity-conserving nucleon-nucleon potentials, namely Hamada-Johnston, Yale, and modified Yale, the circular polarization of the $n - p$ capture $γ$ rays is calculated and compared with the observed value.

RAPID COMMUNICATION

Pseudo-resonance behavior of partial waves in elastic pion scattering

M. M. Hoenig and A. S. Rinat(Reiner)

Phys. Rev. C 10, 2102(R) (1974) - Published 1 November, 1974

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Glauber theory employing observed $π N$ phases is used to compute $π d$ differential cross sections for $E ≲ 600$ MeV. Lacking experimentally extracted phase shifts, we used the model to construct model phases, which have been plotted in Argand diagrams. These display for many $J^{π}$ values a pseudo-resonance behavior. It is restressed that these do not correspond to resonances in a $B = 2$ system but simply reflect a $N^{*}$ in the weakly bound deuteron.

NUCLEAR REACTIONS Calculated $σ_{e l}^{π d} (E, θ)$ ; theoretical phase shift analysis for $E_{π} ≲ 600$ MeV. Interpretation of phase behavior displayed in Argand plots.

RAPID COMMUNICATION

Improved projected Hartree-Fock description of the low-lying quasirotational states in nuclei

F. T. Avignone, III and S. K. Sharma

Phys. Rev. C 10, 2106(R) (1974) - Published 1 November, 1974

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RAPID COMMUNICATION

Improved lifetime measurements in ${}^{61}{Cu}$ via the ${}^{61}{Ni} (p, n γ)$ reaction

R. A. Braga and D. G. Sarantites

Phys. Rev. C 10, 2109(R) (1974) - Published 1 November, 1974

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The effective stopping power for Cu ions slowing in a Ni environment was deduced for an average initial recoil velocity of 0.0025 of $c$ . An improved value of 41 ± 5 fsec for the mean lifetime of the 2088.7-keV level is reported.

NUCLEAR REACTIONS ${}^{61}{Ni} (p, n γ)$ , $E_{p} = 5.3$ MeV, enriched targets; measured $Δ E (τ)$ ; deduced effective stopping power, $τ$ .

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Recent Issues

Fission of odd- $A$ and doubly odd actinide nuclei induced by direct reactions

Levels in ${}^{158}{Gd}$ populated in the decay of 46-min ${}^{158}{Eu}$

Decay of the $K^{π} = 8^{-}$ isomer in ${}^{182}{Hf}$

Half-lives of ${}^{6}{He}$ , ${}^{19}{Ne}$ , and ${}^{42}{Sc}^{m}$

Electric monopole transitions between $0^{+}$ states in ${}^{100}{Ru}$

Coupled-channel calculations of electron scattering by samarium

Decay of ${}^{173}{Hf}$ and measurement of the half-life of the 128.3-keV state in ${}^{173}{Lu}$

Nuclear muon-capture sum rules and mean nuclear excitation energies

Nonassociative algebra in nuclear boson-expansion theory

General boson expansion theory and Lie algebras $B_{n}$ and $D_{n}$

Effect of curvature on nuclear surface energy

Three - body force in the triton

Brueckner-Hartree-Fock calculations and their density dependence

Radius of the neutron distribution in ${}^{208}{Pb}$ from the ( $p, n$ ) quasielastic reaction

Contributions of nucleon momenta to the pion optical potential

$K$ matrix and unitarity constraints on off-shell $T$ matrix elements

Weak parity-nonconserving potentials and circular polarization of $n - p$ capture gamma rays

Pseudo-resonance behavior of partial waves in elastic pion scattering

Improved projected Hartree-Fock description of the low-lying quasirotational states in nuclei

Improved lifetime measurements in ${}^{61}{Cu}$ via the ${}^{61}{Ni} (p, n γ)$ reaction

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