Recent Articles

Generalized BCS calculations for the $2 s - 1 d$ shell with realistic interactions

P. Mpanias and M. L. Rustgi

Phys. Rev. C 16, 816 (1977) - Published 1 August, 1977

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Based on the Hartree-Fock calculations reported earlier, the ground-state properties of $N = Z$ even-even nuclei in the $2 s - 1 d$ shell are investigated within the generalized BCS approach employing $T = 1$ , $T = 0$ , and $T = 1 + T = 0$ pairing correlations and the modified Yale and supersoft core potentials. Comparisons are made with similar less sophisticated calculations reported earlier for the same nuclei using the Yale potential.

NUCLEAR STRUCTURE ${}^{20}{Ne}$ , ${}^{24}{Mg}$ , ${}^{32}S$ , ${}^{36}A$ ; generalized BCS method employing $T = 1$ , $T = 0$ , and $T = 1 + T = 0$ pairing correlations with two different shell-model spaces. Modified Yale and supersoft core interactions.

Comparison of the unitary pole and Adhikari-Sloan expansions in the three-nucleon system

I. R. Afnan and N. D. Birrell

Phys. Rev. C 16, 823 (1977) - Published 1 August, 1977

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The binding energy of ${}^{3}H$ , the percentage $S$ -, $S^{'}$ -, and $D$ -state probability, and the charge form factor of ${}^{3}{He}$ are calculated using the unitary pole and Adhikari-Sloan separable expansions to the Reid soft core potential. Comparison of the results for the two separable expansions show that the expansion of Adhikari and Sloan has the better convergence property, and the lowest rank expansion considered (equivalent to the unitary pole approximation) gives a good approximation to the binding energy of ${}^{3}H$ and the charge form factor of ${}^{3}{He}$ , even at large momentum transfer ( $K^{2} < 20$ ${fm}^{- 2}$ ).

NUCLEAR STRUCTURE ${}^{3}H$ binding energy, ${}^{3}{He}$ charge form factor, Faddeev approach, separable expansion to realistic $N - N$ interactions.

Core polarization in inelastic scattering

F. Petrovich, H. McManus, J. Borysowicz, and G. R. Hammerstein

Phys. Rev. C 16, 839 (1977) - Published 1 August, 1977

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Inelastic scattering is a source of much useful information about core polarization effects in nuclei near closed shells. Although there have been many theoretical treatments of core polarization effects reported in the literature, the results of these calculations have rarely been applied to the interpretation of inelastic scattering data. In the present paper we review the microscopic models for the treatment of inelastic proton and electron scattering and the microscopic models for the treatment of core polarization. Estimates are made of core excited admixtures in the wave functions for low-lying states in ${}^{42}{Ca}$ , ${}^{50}{Ti}$ , ${}^{89}Y$ , ${}^{90}{Zr}$ , ${}^{207}{Pb}$ , and ${}^{209}{Bi}$ . The resulting wave functions are used to calculate theoretical ( $p, p^{'}$ ) cross sections and ( $e, e^{'}$ ) form factors for comparison with available experimental data. "Realistic" $G$ matrix interactions are used as the starting point in both the structure and the ( $p, p^{'}$ ) calculations. In the structure calculations the interaction is modified by means of a "bootstrap" prescription to account for important long-range core correlations and in the ( $p, p^{'}$ ) calculations it is modified by the addition of an imaginary component. It is concluded that the overall features of the experimental data can be understood from these calculations.

NUCLEAR STRUCTURE, NUCLEAR REACTIONS ( $p, p^{'}$ ) and ( $e, e^{'}$ ); nuclei near closed shells; microscopic model for core polarization; calculated $σ (θ)$ and $F (q)$ .

Short-range correlations and pseudopotentials. V

Ahmed Osman

Phys. Rev. C 16, 873 (1977) - Published 1 August, 1977

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Deformed Hartree-Fock-Bogoliubov calculations have been carried out with an effective interaction derived from the different Hamada-Johnson, Yale, Tabakin, and Reid potentials and from the potential $A$ calculated by us. Short-range pseudopotentials are introduced to these potentials to achieve healing in the correlated wave functions and to produce zero-phase shift in the pair state. The deformed Hartree-Fock-Bogoliubov method has been applied to the $2 p - 1 f$ shell even-even nuclei. Intrinsic quadrupole moments $〈 Q_{0}^{2} 〉$ , quadrupole moments of the first excited states $Q_{2 +}$ , and the reduced transition probabilities $B (E 2) (0^{+} \to 2^{+})$ have been calculated. The angular momentum projected spectra for these nuclei have also been obtained. The present calculations of quadrupole moments, transition probabilities, and angular momentum spectra for the different Ti, Cr, Fe, and Ni isotopes are in good agreement with the experimental results.

NUCLEAR STRUCTURE ${}^{44, 46, 48, 50}{Ti}$ , ${}^{48, 50, 52, 54}{Cr}$ , ${}^{52, 54, 56, 58}{Fe}$ , ${}^{58, 60, 62, 64}{Ni}$ ; calculated intrinsic quadrupole moments, quadrupole moments of the first excited states, reduced transition probabilities, projected angular momentum spectra and energy levels; pseudopotentials. Hartree-Fock-Bogoliubov method.

Density compression in colliding nuclear slabs

Gottfried Holzwarth

Phys. Rev. C 16, 885 (1977) - Published 1 August, 1977

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RAPID COMMUNICATION

Half-life of ${}^{17}F$

David E. Alburger

Phys. Rev. C 16, 889(R) (1977) - Published 1 August, 1977

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RAPID COMMUNICATION

Reaction cross sections for ${}^{16}O$ + ${}^{16}O$

J. J. Kolata, R. C. Fuller, R. M. Freeman, F. Haas, B. Heusch, and A. Gallmann

Phys. Rev. C 16, 891(R) (1977) - Published 1 August, 1977

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The total fusion cross section $σ_{f}$ for ${}^{16}O$ + ${}^{16}O$ has been measured in 500 keV steps between 12.5 and 30.5 MeV c.m. energy via $γ$ -ray techniques. The excitation function for $σ_{f}$ shows clear evidence of periodic structure between 14 and 28 MeV (c.m.), as predicted by the optical model. These oscillations are out of phase with those observed in 90° elastic scattering. Individual yields of 12 nuclides formed in the reaction were also obtained. The narrow ( $Γ < 1$ MeV) resonance at $E_{c . m .} = 26.5$ MeV, which is correlated in the ${}^{20}{Ne}$ and ${}^{16}O$ ( $3^{-}$ ) channels, is suggested to be an "α-exchange" resonance.

NUCLEAR REACTIONS ${}^{16}O$ + ${}^{16}O$ 12.5-30.5 MeV (c.m.); measured excitation functions for production of $A = 16 - 31$ reaction products; deduced evidence for broad shape resonances, and a narrow resonance at $E_{c . m .} = 26.5$ MeV.

RAPID COMMUNICATION

Effective three-body interaction in ${}^{93}{Tc}$ , ${}^{93}{Mo}$ , and ${}^{94}{Ru}$

H. A. Mavromatis, L. D. Skouras, and C. Dedes

Phys. Rev. C 16, 895(R) (1977) - Published 1 August, 1977

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RAPID COMMUNICATION

Magnetic moments of the $2^{+}$ first excited states of even iron isotopes

J. M. Brennan, N. Benczer-Koller, M. Hass, and H. T. King

Phys. Rev. C 16, 899(R) (1977) - Published 1 August, 1977

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The large magnetic fields that act on fast-moving ions traversing thin magnetized Fe foils were utilized to remeasure the magnetic moments of the first excited $2^{+}$ states of ${}^{54}{Fe}$ and ${}^{58}{Fe}$ . The technique reported here does not require an accurate knowledge of the nuclear lifetime and does not depend on the static magnetic field of Fe in Fe. Assuming $g ({}^{56}{Fe}, 2^{+}) = 0.61 \pm 0.08$ , we obtain $g = 1.68 \pm 0.38$ and $g = 0.46 \pm 0.10$ for the first $2^{+}$ states of ${}^{54}{Fe}$ and ${}^{58}{Fe}$ , respectively. The present results agree well with previous measurements and support the existing models for the structure of these states.

NUCLEAR REACTIONS ${}^{54, 56, 58}{Fe}$ ( ${}^{32}S$ , ${}^{32}{S'}$ ) ${}^{54, 56, 58}{Fe}^{*}$ ( $2_{1}^{*}$ ) $E = 72$ MeV, enriched targets; measured $W (θ, H, \infty)$ in polarized iron. Deduced $g ({}^{54}{Fe}, 2_{1}^{+}) = 1.68 \pm 0.38$ , $g ({}^{58}{Fe}, 2_{1}^{+}) = 0.43 \pm 0.10$ .

RAPID COMMUNICATION

Quadrupole transfer strength studied through heavy-ion induced two-neutron transfer between the shape transitional nuclei ${}^{190, 192}{Os}$

D. L. Hanson, K. A. Erb, J. S. Vaagen, R. J. Ascuitto, D. A. Bromley, and J. J. Kolata

Phys. Rev. C 16, 902(R) (1977) - Published 1 August, 1977

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A coupled-channels Born-approximation analysis of the reaction ${}^{192}{Os}$ ( ${}^{12}C$ , ${}^{14}C$ ) ${}^{190}{Os}$ at $E_{lab} = 70$ MeV demonstrates that the direct quadrupole transfer strength is very weak, in continuation of the trend found previously in a study of the tungsten nuclei. Elastic and inelastic scattering data for the ${}^{12}C$ channel were also taken and analyzed in a conventional coupled-channels model to determine the relative motion.

NUCLEAR REACTIONS ${}^{192}{OS}$ ( ${}^{12}C$ , ${}^{12}C$ ), ${}^{192}{OS}$ ( ${}^{12}C$ , ${}^{14}C$ ), $E_{lab} = MeV$ , measured $σ (Θ)$ . CCBA analysis. Demonstrated effect of shape transitions on quadrupole transfer strength.

RAPID COMMUNICATION

Simple cure to the breakdown of constrained Hartree-Fock

B. G. Giraud and J. LeTourneux

Phys. Rev. C 16, 906(R) (1977) - Published 1 August, 1977

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The doubly constrained Hamiltonian $H - λ Q + μ Q^{2}$ with $μ > 0$ has a ground state even when the observable $Q$ , being unbounded, leads to a breakdown of the traditional variational calculation with a single linear constraint. The additional term $μ Q^{2}$ is not just a mathematical device but ensures that the variational solutions are confined reasonably close to the origin.

NUCLEAR STRUCTURE Breakdown of Hartree-Fock calculations with a constraint on an unbounded operator.

RAPID COMMUNICATION

Nucleon form factors, Lorentz invariance, and nuclear photoabsorption

J. L. Friar and S. Fallieros

Phys. Rev. C 16, 908(R) (1977) - Published 1 August, 1977

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The role of the intrinsic nucleon size in a phenomenological treatment of photon absorption by a nucleus is discussed. It is suggested that the complete transition matrix element should be written as a product of the purely nuclear matrix element and the intrinsic nucleon form factor. The latter is written as a function, not of $q^{2}$ (the four-momentum transfer), but of $q^{2} + ω^{2}$ , where $ω$ is the excitation energy of the nucleus. We note that for real photons where $q^{2} = 0$ this is essentially equivalent to ${\vec{q}}^{2}$ , i.e., the three-momentum transfer.

NUCLEAR REACTIONS Nucleon form factor, phenomenology, relativistic invariance, photonuclear cross sections.

RAPID COMMUNICATION

Is it safe to use the unitary pole expansion for hard core potentials?

A. N. Mantri and A. V. Lagu

Phys. Rev. C 16, 912(R) (1977) - Published 1 August, 1977

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We have examined the various terms in the unitary pole expansion for a hard core potential. It is found that the goodness of the unitary pole expansion depends upon the number of positive and negative eigenvalues in the expansion. It is doubtful if the unitary pole expansion improves over the one term approximation in such a case.

NUCLEAR STRUCTURE $t$ matrix, unitary pole expansion, unitary pole approximation, hard core potentials.

RAPID COMMUNICATION

Mass measurements of the proton-rich nuclei ${}^{50}{Fe}$ and ${}^{54}{Ni}$

R. E. Tribble, J. D. Cossairt, D. P. May, and R. A. Kenefick

Phys. Rev. C 16, 917(R) (1977) - Published 1 August, 1977

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The reactions ${}^{54}{Fe}$ ( ${}^{4}{He}$ , ${}^{8}{He}$ ) ${}^{50}{Fe}$ and ${}^{58}{Ni}$ ( ${}^{4}{He}$ , ${}^{8}{He}$ ) ${}^{54}{Ni}$ have been observed at an incident $α$ energy of 110 MeV. The reaction $Q$ values are found to be $Q ({}^{50}{Fe}) = - 50.95 \pm 0.06$ MeV and $Q ({}^{54}{Ni}) = - 50.19 \pm 0.05$ MeV. The experiments provide the first observation and subsequent mass measurement of the proton-rich nuclei ${}^{50}{Fe}$ and ${}^{54}{Ni}$ .

NUCLEAR REACTIONS ${}^{54}{Fe}$ ( ${}^{4}{He}$ , ${}^{8}{He}$ ) and ${}^{54}{Ni}$ ( ${}^{4}{He}$ , ${}^{8}{He}$ ). Measured reaction $Q$ values and mass excesses of ${}^{50}{Fe}$ and ${}^{54}{Ni}$ .

Erratum: ${}^{14}N ({}^{7}{Li}, t) {}^{18}F$ reaction and the 4p-2h, $K^{π} = 1^{+}$ rotational band in ${}^{18}F$

M. E. Cobern and P. D. Parker

Phys. Rev. C 16, 920 (1977) - Published 1 August, 1977

Resonating-group study of $p + α$ scattering from 68 to 125 MeV

D. R. Thompson, Ronald E. Brown, M. LeMere, and Y. C. Tang

Phys. Rev. C 16, 1 (1977) - Published 1 July, 1977

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The resonating-group method, together with a phenomenological consideration of reaction effects, is used to analyze $p + α$ scattering data at the relatively high c.m. energies of 68, 80, and 124.8 MeV. The nucleon-nucleon potential employed contains a weakly repulsive core and yields a reasonably satisfactory description of not only the two-nucleon scattering data but also the essential properties of the $α$ particle. The result shows that satisfactory agreement with experiment can be obtained. In particular, it is found that, because of the use of a totally antisymmetric wave function, the scattering behavior at large angles is adequately described.

[NUCLEAR REACTIONS ${}^{4}{He} (p, p)$ , $E = 68, 80, and 124.8$ MeV (c.m.); calculated phase shifts and $σ (θ)$ . Resonating-group method.]

Analysis of polarization and analyzing power in the reaction ${}^{3}H (p, n) {}^{3}{He}$

J. J. Bevelacqua

Phys. Rev. C 16, 107 (1977) - Published 1 July, 1977

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The difference between the polarization and analyzing power for the reaction ${}^{3}{He} (p, n) {}^{3}{He}$ has been calculated in a $4 ℏ ω$ model space within the framework of the generalized $R$ -matrix method of Lane and Robson. The model calculations indicate neither the presence of $f$ wave components nor a significant sensitivity of the $P - A$ difference to the position of the ${}^{4}{He}$ levels.

[NUCLEAR REACTIONS $P^{y} - A_{y}$ difference for the ${}^{3}H (p, n) {}^{3}{He}$ reaction.]

Low-lying levels of ${}^{98}{Tc}$

D. E. Miracle, E. C. Hagen, and B. D. Kern

Phys. Rev. C 16, 111 (1977) - Published 1 July, 1977

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The levels of ${}^{98}{Tc}$ have been investigated through the ${}^{98}{Mo} (p, n γ) {}^{98}{Tc}$ reaction with detection of the $γ$ rays. Excitation functions and $γ - γ$ coincidence spectra were used in determining the energies of the levels. A pulsed beam was used in obtaining the spectrum of the delayed radiation from the 14.6-μsec isomeric level. Thirty-four $γ$ rays have been assigned to twenty-three excited levels of ${}^{98}{Tc}$ .

[NUCLEAR REACTIONS ${}^{98}{Mo} (p, n γ)$ , $E_{p} = 2.513 - 3.620$ MeV; measured $E_{γ}$ , $γ - γ$ coincidences, delayed $γ$ . ${}^{98}{Tc}$ deduced levels. Enriched target.]

Negative-parity yrast states in ${}^{150}{Gd}$

D. R. Haenni and T. T. Sugihara

Phys. Rev. C 16, 120 (1977) - Published 1 July, 1977

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High-spin states populated by the ${}^{150}{Sm} (α, 4 n) {}^{150}{Gd}$ reaction have been studied by in-beam $γ$ -ray and conversion-electron spectroscopy. Conversion-electron data for the decay of 5.8-min ${}^{150}{Tb}$ to levels in ${}^{150}{Gd}$ have also been obtained. The proposed level scheme for ${}^{150}{Gd}$ includes 21 levels, 11 of which are previously unreported. A sequence of odd-spin negative-parity states from $17^{-}$ to $3^{-}$ carries most of the yrast-cascade intensity. This sequence is interpreted as containing two quasirotational bands. The states below $11^{-}$ represent a band built on an octupole vibration while those above $11^{-}$ constitute a band built on an $ν (i_{\frac{13}{2}} h_{\frac{9}{2}}) 11^{-}$ , quasiparticle state. Other quasiparticle states arising from the $ν (i_{\frac{13}{2}} h_{\frac{9}{2}})$ and $ν (f_{\frac{7}{2}} h_{\frac{9}{2}})$ configurations are proposed.

[NUCLEAR REACTIONS ${}^{150}{Sm} (α, 4 n)$ , $E_{α} = 45 - 55$ MeV and ${}^{152}{Sm} (α, 6 n)$ , $E_{α} = 77$ MeV; measured $E_{γ}$ , $I_{γ} (θ)$ , $I_{γ} (t)$ , $I_{γ} (E)$ , $I_{ce}$ , $γ - γ$ coin. ${}^{150}{Gd}$ deduced levels, ICC, $J$ , $π$ .

RADIOACTIVITY 5.8-min ${}^{150}{Tb}$ [from ${}^{151}{Eu} ({}^{3}{He}, 4 n)$ ] measured $I_{ce}$ . ${}^{150}{Gd}$ deduced ICC, $J$ , $π$ . Enriched targets, Ge(Li), Si(Li) detectors.]

Partial widths and gamma-ray decay of the 2883- and 5037-keV levels in ${}^{41}{Sc}$

R. L. Kozub, B. E. Cooke, J. R. Leslie, and B. C. Robertson

Phys. Rev. C 16, 132 (1977) - Published 1 July, 1977

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Proton and $γ$ -ray decay widths for the ${7 / 2}^{+}$ resonance at 2883 keV excitation in ${}^{41}{Sc}$ have been deduced from measurements of $\frac{Γ_{γ}}{Γ}$ and the ( $p, γ$ ) resonance strength. Our results are $Γ_{γ} = 0.058 \pm 0.007$ eV and $Γ_{p} = 0.090 \pm 0.011$ eV. Angular distributions measured for the $5037 (\frac{9}{2^{+}}) \to 2883$ keV and $2883 \to 0 (\frac{7}{2^{-}})$ keV transitions confirm the $J = \frac{7}{2}$ assignment for the 2883-keV level. The linear polarization was measured for the $2883 \to 0$ keV transition and confirms the positive parity assignment. In addition, the ( $p, γ$ ) strength for the 5037-keV level was measured, and our strength results for both resonances are lower than those of Youngblood, Wildenthal, and Class by a factor of 1.4.

[NUCLEAR REACTIONS ${}^{40}{Ca} (p, γ)$ , $E_{p} = 1.84, 4.05$ MeV; measured $σ (E_{γ}, θ)$ , $Q$ , $P (90^{\circ})$ , resonance strengths, $I_{γ}$ . ${}^{41}{Sc}$ deduced levels, $J^{π}$ , $Γ_{γ}$ , $Γ_{p}$ , $C {}^{2}S_{p}$ . Enriched target.]

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Recent Issues

Generalized BCS calculations for the $2 s - 1 d$ shell with realistic interactions

Comparison of the unitary pole and Adhikari-Sloan expansions in the three-nucleon system

Core polarization in inelastic scattering

Short-range correlations and pseudopotentials. V

Density compression in colliding nuclear slabs

Half-life of ${}^{17}F$

Reaction cross sections for ${}^{16}O$ + ${}^{16}O$

Effective three-body interaction in ${}^{93}{Tc}$ , ${}^{93}{Mo}$ , and ${}^{94}{Ru}$

Magnetic moments of the $2^{+}$ first excited states of even iron isotopes

Quadrupole transfer strength studied through heavy-ion induced two-neutron transfer between the shape transitional nuclei ${}^{190, 192}{Os}$

Simple cure to the breakdown of constrained Hartree-Fock

Nucleon form factors, Lorentz invariance, and nuclear photoabsorption

Is it safe to use the unitary pole expansion for hard core potentials?

Mass measurements of the proton-rich nuclei ${}^{50}{Fe}$ and ${}^{54}{Ni}$

Erratum: ${}^{14}N ({}^{7}{Li}, t) {}^{18}F$ reaction and the 4p-2h, $K^{π} = 1^{+}$ rotational band in ${}^{18}F$

Resonating-group study of $p + α$ scattering from 68 to 125 MeV

Analysis of polarization and analyzing power in the reaction ${}^{3}H (p, n) {}^{3}{He}$

Low-lying levels of ${}^{98}{Tc}$

Negative-parity yrast states in ${}^{150}{Gd}$

Partial widths and gamma-ray decay of the 2883- and 5037-keV levels in ${}^{41}{Sc}$

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