Recent Articles

$σ$ model in the many-body problem

Hirokazu Tezuka

Phys. Rev. C 24, 288 (1981) - Published 1 July, 1981

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The linear $σ$ model is applied to the many-body problem. The masses of nucleons, sigma mesons, and pions depend on the nucleon density. It is shown that the effective pion mass becomes naught at much lower density than the normal density. This suggests that pions condense at the normal density. Thus we must take pion condensation into consideration when we apply this model to the many-body problem.

[NUCLEAR STRUCTURE $σ$ model is applied to many-body problem considering nucleon mean field.]

Exact multiple scattering theory of two-nucleus collisions including the Pauli principle

S. A. Gurvitz

Phys. Rev. C 24, 29 (1981) - Published 1 July, 1981

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Exact equations for two-nucleus scattering are derived in which the effects of the Pauli principle are fully included. Our method exploits a modified equation for the scattering of two identical nucleons, which is obtained at the beginning. Considering proton-nucleus scattering we found that the resulting amplitude has two components, one resembling a multiple scattering series for distinguishable particles, and the other a distorted ( $A - 1$ ) nucleon cluster exchange. For elastic $pA$ scattering the multiple scattering amplitude is found in the form of an optical potential expansion. We show that the Kerman-McManus-Thaler theory of the optical potential could be easily modified to include the effects of antisymmetrization of the projectile with the target nucleons. Nucleus-nucleus scattering is studied first for distinguishable target and beam nucleus. Afterwards the Pauli principle is included, where only the case of deuteron-nucleus scattering is discussed in detail. The resulting amplitude has four components. Two of them correspond to modified multiple scattering expansions and the others are distorted ( $A - 1$ )- and ( $A - 2$ )- nucleon cluster exchange. The result for $d - A$ scattering is extended to the general case of nucleus-nucleus scattering. The equations are simple to use and as such constitute an improvement over existing schemes.

[NUCLEAR REACTIONS $p - p$ scattering, $p$ -nucleus scattering, multiple scattering series, antisymmetrization, optical potential, deuteron-nucleus scattering, nucleus-nucleus scattering.]

Isomeric and high-spin states of ${}^{94}{Tc}$ and the search for yrast isomers near $N \sim 50$

I. Y. Lee, N. R. Johnson, F. K. McGowan, G. R. Young, M. W. Guidry, and S. W. Yates

Phys. Rev. C 24, 293 (1981) - Published 1 July, 1981

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A search for isomers in the $N \sim 50$ region has produced no evidence of high-spin yrast isomerism. A new 4.5-ns low-multiplicity isomer has been identified and assigned to ${}^{94}{Tc}$ , while the yrast sequence of ${}^{94}{Tc}$ has been established to more than 5 MeV in excitation energy.

[NUCLEAR REACTIONS ${}^{76}{Ge}$ , ${}^{78}{Se} ({}^{20}{Ne}, x n y p γ)$ , $E = 80.9$ MeV, ${}^{89}Y$ , ${}^{93}{Nb} ({}^{10}B, x n y p γ)$ , $E = 52.0, 58.4, 62.8$ MeV; measured $E_{γ}$ , $I_{γ}$ , $γ - γ$ prompt and delayed coin, $γ - X$ coin; deduced levels, $t_{\frac{1}{2}}$ of ${}^{94}{Tc}$ isomer, yrast states.]

Beta-ray branching in the decay of ${}^{20}F$

D. E. Alburger and E. K. Warburton

Phys. Rev. C 24, 296 (1981) - Published 1 July, 1981

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Measurements on the $γ$ -ray spectrum from 11-sec ${}^{20}F$ resulted in an energy of 3332.51(19) keV for the cascade $γ$ ray from the ${}^{20}{Ne}$ 4.97-MeV state and a $β$ -branching intensity to this level of 0.90(4) × $10^{- 4}$ per decay. The corresponding $log f_{0} t$ value is 7.16(2), and the excitation energy of the ${}^{20}{Ne}$ state is 4966.51(20) keV.

[RADIOACTIVITY ${}^{20}F$ ; measured $E_{γ}$ , $I_{γ}$ ; Ge(Li) detector; deduced $E_{x}$ , $β$ branching, and $log f_{0} t$ value.]

Half-lives of ${}^{199}{Rn}$ and ${}^{199}{Rn}^{m}$

H. A. Enge, M. K. Salomaa, A. Sperduto, W. Schier, and H. E. Wegner

Phys. Rev. C 24, 298 (1981) - Published 1 July, 1981

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The nuclide ${}^{199}{Rn}$ and the isomer ${}^{199}{Rn}^{m}$ were produced in the reaction ${}^{169}{Tm} ({}^{35}{Cl}, 5 n) {}^{199}{Rn}$ . An electromagnetic velocity filter separated the recoiling residual nuclei from the beam at zero degree. The nuclei were embedded into a surface-barrier detector recording both the arrival pulse and the alpha-decay event. The half-life for ${}^{199}{Rn}$ in its presumed ground state ( $E_{a} = 6.99$ MeV) has been determined as 0.5 ± 0.2 sec and the half-life of ${}^{199}{Rm}^{m}$ ( $E_{a} = 7.06$ MeV) is 0.29 ± 0.05 sec.

[RADIOACTIVITY ${}^{199}{Rn}$ and ${}^{199}{Rn}^{m}$ ; measured half-lives.]

Analysis of $π^{0}$ photoproduction measurements near threshold on light nuclei

P. Argan, G. Audit, A. Bloch, N. de Botton, J. L. Faure, C. Schuhl, G. Tamas, C. Tzara, E. Vincent, J. Deutsch, D. Favart, R. Prieels, and B. Van Oystaeyen

Phys. Rev. C 24, 300 (1981) - Published 1 July, 1981

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Our recently published $π^{0}$ photoproduction data at threshold have been reanalyzed with the use of a more refined detection efficiency calculation. The high energy points appear to be consistent with the threshold measurements; the effective threshold amplitudes remain unchanged, and are now supported by the complete set of experimental data.

[NUCLEAR REACTIONS ( $γ, π^{0}$ ), ${}^{1}H$ , ${}^{2}H$ , ${}^{3}{He}$ , and ${}^{4}{He}$ targets; measured reaction yields, $E_{π 0} = 1 - 10$ MeV.]

Surface coefficients of Skyrme-Orsay forces

M. Farine, J. Côté, and J. M. Pearson

Phys. Rev. C 24, 303 (1981) - Published 1 July, 1981

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Hartree-Fock calculations of asymmetric semi-infinite nuclear matter are performed for all the Skyrme-Orsay forces, with inclusion of the spin-orbit term. Values of $Q$ obtained from the surface energy are in reasonable agreement with those found from the neutron-skin thickness.

[NUCLEAR STRUCTURE Surface droplet-model parameters determined by Hartree-Fock calculations on semi-infinite nuclear matter with all Skyrme-Orsay forces.]

Pion photoproduction on ${}^{27}{Al}$ : The effect of $V_{opt}$

N. Freed and P. Ostrander

Phys. Rev. C 24, 306 (1981) - Published 1 July, 1981

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Total cross sections for pion photoproduction to bound states in ${}^{27}{Mg}$ are calculated in the distorted wave impulse approximation and compared to experiment. Particular attention is paid to the form of the optical potential used to incorporate final state effects. Substantial differences are found between results using an earlier potential and present results using potentials having different analytic forms. The latter lead to good agreement with experiment.

[NUCLEAR REACTIONS ${}^{27}{Al} (γ, π^{+})$ . Calculated total cross sections; effects of pion optical potential.]

RAPID COMMUNICATION

Search for a fusion $L$ window in the ${}^{16}O$ + ${}^{16}O$ system at $E_{c . m .} = 34$ MeV

A. Lazzarini, H. Doubre, K. T. Lesko, V. Metag, A. Seamster, R. Vandenbosch, and W. Merryfield

Phys. Rev. C 24, 309(R) (1981) - Published 1 July, 1981

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We have measured the inelastic scattering cross section for the reaction ${}^{16}O$ ( ${}^{16}O$ , ${}^{16}O$ ') ${}^{16}O$ . The inelastic yield is dominated by single and double excitation of the group of states with $6.1 <~ E_{x} <~ 7.1$ MeV in ${}^{16}O$ . The yield for energy losses greater than 15 MeV is 5.9 mb. This is significantly less than time-dependent Hartree-Fock calculations indicate for this system where nonfusion for low partial waves is predicted.

[NUCLEAR REACTIONS ${}^{16}O$ ( ${}^{16}O$ , ${}^{16}O$ ′), $E_{c . m .} = 34$ MeV, $σ (E_{x}, θ_{c . m .})$ ; $θ_{c . m .} = 30^{\circ} - 90^{\circ}$ , $E_{x} = 0 - 20$ MeV, inelastic yields compared to TDHF.]

RAPID COMMUNICATION

${\frac{1}{2}}^{+} \to {\frac{1}{2}}^{-}$ beta decay of ${}^{19}{Ne}$ and the parity nonconserving $NN$ force

E. G. Adelberger, M. M. Hindi, C. D. Hoyle, H. E. Swanson, and R. D. Von Lintig

Phys. Rev. C 24, 313(R) (1981) - Published 1 July, 1981

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We obtain a branching ratio of (1.20 ± 0.20) × $10^{- 4}$ for the $β^{+}$ decay of ${}^{19}{Ne}$ to the 110 keV ${\frac{1}{2}}^{-}$ level of ${}^{19}F$ . This transition (presumably dominated by the $Δ J^{π} = 0^{-}$ axial charge operator) provides a crucial test of wave functions used in interpreting the parity mixing of the ground and 110 keV levels of ${}^{19}F$ . These wave functions, which yield a parity mixing larger than that observed experimentally, also predict too large a $β^{+}$ decay rate.

[RADIOACTIVITY ${}^{19}{Ne}$ ; measured branch to ${}^{19}F$ (110 keV); deduced $ft$ . Compared to shell model calculation.]

RAPID COMMUNICATION

Confirmation of the photoneutron cross section for ${}^{4}{He}$ below 33 MeV

L. Ward, D. R. Tilley, D. M. Skopik, N. R. Roberson, and H. R. Weller

Phys. Rev. C 24, 317(R) (1981) - Published 1 July, 1981

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A recently reported measurement of the photoneutron cross section for ${}^{4}{He}$ indicates a value of about 1.0 mb for $E_{x}$ of ∼23 to ∼33 MeV. This result, when combined with the previously reported ( $γ, p$ ) cross section in this energy region, implies a ( $γ, p$ )-to-( $γ, n$ ) cross section ratio of 1.6 to 1.9 in the 26 to 29 MeV region of ${}^{4}{He}$ . We have used the inverse reaction ${}^{3}{He} (n, γ) {}^{4}{He}$ to measure the photoneutron cross section for ${}^{4}{He}$ . Our detailed balanced results confirm the recently reported measurements.

[NUCLEAR REACTIONS ${}^{3}{He} (n, γ) {}^{4}{He}$ ; measured $σ (E; θ)$ , $E = 6.0 to 17.0$ MeV. Results confirm the most recent ${}^{4}{He} (γ, n) {}^{3}{He}$ measurements.]

RAPID COMMUNICATION

Heavy ion resonances in mismatched channels

O. Tanimura and U. Mosel

Phys. Rev. C 24, 321(R) (1981) - Published 1 July, 1981

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Recently measured cross sections for inelastic $0_{2}^{+}$ and $3^{-}$ excitations in ${}^{16}O$ + ${}^{16}O$ are analyzed in the framework of coupled channel calculations. The correlation between the peaks in both channels is explained in terms of a strongly mixed resonant state of the nucleus-nucleus system. The equivalent local potentials including the channel couplings are calculated for each channel. The resonances are seen to arise in all channels simultaneously at the barrier tops of these effective potentials.

[NUCLEAR REACTIONS ${}^{16}O$ ( ${}^{16}O$ , ${}^{16}O$ ), $E = 20 - 40$ MeV; calculated $σ (E)$ ; inelastic excitations. Coupled channels method, strong coupling.]

Erratum: Deuteron photodisintegration: Impulse approximation and gauge invariance

W-Y. P. Hwang and Gerald A. Miller

Phys. Rev. C 24, 325 (1981) - Published 1 July, 1981

Alternative to Padé technique for solving scattering integral equations

Lauro Tomio and Sadhan K. Adhikari

Phys. Rev. C 24, 43 (1981) - Published 1 July, 1981

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The aim of this work is to show how we can improve systematically the rate of convergence of a recently proposed method for iterative solution of scattering integral equations. The method relies on the introduction of an auxiliary equation containing an arbitrary function, whose kernel is much weaker than that of the original equation. The solution of the original equation is then expressed in terms of that of the auxiliary equation which is supposed to have a convergent iterative solution. In this work we introduce successive subtractions in the kernel in order to make it weaker. Such subtractions in the kernel are very simple to implement in practice and the present method appears to have some advantage over the other existing methods. We explain how to generalize the method for multichannel scattering equations. Using the present method we show how to modify a method by Fuda for three-particle scattering equations in order to have a method which uses the iterative solution only of nonsingular equations above the three-body breakup threshold. The method is used numerically to compute phase shifts, scattering lengths, and fully off-shell $t$ matrix elements for neutron-deuteron scattering in the $s$ -wave Amado model and for nucleon-nucleon scattering with the Reid ${}^{1}S_{0}$ potential. The iterative solution of the auxiliary equation is found to converge much faster than the conventional Padé technique in the case of the neutron-deuteron scattering and yields results with high precision.

[NUCLEAR REACTIONS Multichannel scattering equations, iterative solution of auxiliary equations, Reid ${}^{1}S_{0}$ potential, Amado model, off-shell $t$ matrix elements and phase shifts computed.]

Collective and neutron-structure effects in the elastic scattering of vector polarized deuterons in the $A = 90$ mass region

J. A. Bieszk and J. Ulbricht

Phys. Rev. C 24, 56 (1981) - Published 1 July, 1981

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The analyzing power has been measured for elastic scattering of vector-polarized deuterons from ${}^{92, 94, 96}{Zr}$ and ${}^{92}{Mo}$ at $E_{d} = 12$ MeV. Previous measurements on ${}^{88}{Sr}$ and ${}^{98}{Mo}$ have been extended. The present data combined with published measurements on ${}^{90, 91}{Zr}$ and ${}^{76, 78, 80, 82}{Se}$ show that these angular distributions can be explained only if one considers both collective and neutron structure-dependent effects.

[NUCLEAR REACTIONS ${}^{92, 94, 96}{Zr}$ , ${}^{92, 98}{Mo}$ , ${}^{88}{Sr} (d, d)$ , $E = 12.0$ MeV; measured $i T_{11} (θ)$ . Enriched targets.]

${}^{40}{Ca} (d, {}^{3}{He}) {}^{39}K$ reaction at 76 MeV

D. W. Devins, D. L. Friesel, W. P. Jones, A. C. Attard, S. F. Collins, G. G. Shute, B. M. Spicer, V. C. Officer, I. D. Svalbe, R. S. Henderson, and W. E. Dollhopf

Phys. Rev. C 24, 59 (1981) - Published 1 July, 1981

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The differential cross sections of the ${}^{3}{He}$ groups emitted in the ${}^{40}{Ca} (d, {}^{3}{He}) {}^{39}K$ reaction have been measured at a bombarding energy of 76 MeV. The ${}^{3}{He}$ particles were measured with an energy resolution of 55 keV. Differential cross sections were fitted using a distorted wave program and spectroscopic factors were deduced for several proton hole states of ${}^{39}K$ . The single hole final states essentially exhaust the sum rule for the $1 d_{\frac{3}{2}}$ , $2 s_{\frac{1}{2}}$ , and $1 d_{\frac{5}{2}}$ subshells. Because of the strong absorption of ${}^{3}{He}$ particles in nuclear matter, this reaction is a surface reaction, and as such populates only the outer shells. By contrast, the ${}^{40}{Ca} (p, 2 p)$ reaction is able to populate all proton hole states, including those of the $1 p$ and $1 s$ shells. The population of the quartet of odd parity states, which from a nuclear structure point of view consist of a ${1 d}_{\frac{3}{2}}$ hole coupled to the $3^{-}$ state of ${}^{40}{Ca}$ , was observed. The differential cross sections for the ${}^{3}{He}$ groups populating those states were calculated using a coupled channels program and these calculations are in satisfactory agreement with the experimental results.

[NUCLEAR REACTIONS ${}^{40}{Ca} (d, {}^{3}{He})$ , $E = 76$ MeV; measured $σ (θ)$ , enriched target. DWBA and CCBA analysis, deduced spectroscopic factors.]

Coulomb wave expansion in electron scattering

P. Durgapal and D. S. Onley

Phys. Rev. C 24, 7 (1981) - Published 1 July, 1981

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Coulomb waves are the solutions of the Dirac equation with a point-charge potential and are known analytic functions (Whittaker Functions). A number of matrix elements involving two Coulomb waves can be evaluated analytically, making the Coulomb waves basis an attractive alternative to the distorted wave basis. The difference between the point-charge potential and the distributed charge potential is treated as a perturbation. Phase shifts are calculated analytically for a distribution of the form $P (x) \exp (- a x)$ , where $P (x)$ is a polynomial. Also calculated are radial integrals for electric monopole and quadrupole excitations in the same approximation. Scattering cross sections are compared with the conventional distorted wave calculations. The approximation works best for large angular momentum partial waves or low momentum transfer. It could not, in general, replace distorted wave calculations for the lowest partial waves but it could serve to restrict numerical calculations to this range, or it could be used for total cross sections and calculations of radiative corrections.

[NUCLEAR REACTIONS ( $e, e$ ), ( $e, e^{'}$ ) $E 0$ , $E 2$ cross sections calculated. Matrix elements involving Coulomb waves evaluated analytically.]

Analysis of precompound processes in ( $p, n$ ) reactions with the statistical multistep direct emission theory

R. Bonetti, M. Camnasio, L. Colli Milazzo, and P. E. Hodgson

Phys. Rev. C 24, 71 (1981) - Published 1 July, 1981

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The fully quantum-mechanical statistical multistep direct emission theory of Feshbach, Kerman, and Koonin is used to analyze the differential cross sections of ( $p, n$ ) reactions on ${}^{48}{Ca}$ , ${}^{90}{Zr}$ , ${}^{120}{Sn}$ , and ${}^{208}{Pb}$ from 25 to 45 MeV. The interacting particles are described by distorted waves and the interactions inside the nucleus are described by a single-particle model. The absolute magnitudes, as well as the angular variations of the continuum spectra, are well reproduced and the relative contributions of single and multistep processes are evaluated.

[NUCLEAR REACTIONS ${}^{48}{Ca}$ , ${}^{90}{Zr}$ , ${}^{120}{Sn}$ , ${}^{208}{Pb}$ ( $p, n$ ). Calculated cross sections and angular distributions. Deduced two-body interaction strength.]

Charge and transition densities for the samarium isotopes by electron scattering

M. A. Moinester, J. Alster, G. Azuelos, J. B. Bellicard, B. Frois, M. Huet, P. Leconte, and Phan Xuan Ho

Phys. Rev. C 24, 80 (1981) - Published 1 July, 1981

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We analyzed 251.5 and 401.4 MeV electron scattering data on ${}^{144, 148, 150, 152}{Sm}$ . The momentum transfer ranged from 0.6 to 2.5 ${fm}^{- 1}$ . These isotopes span the transition region from the spherical ${}^{144}{Sm}$ to the deformed ${}^{152}{Sm}$ . Ground state charge distributions and lowest $2^{+}$ state transition charge densities were determined via a phase shift analysis for elastic scattering and distorted-wave Born approximation calculations for inelastic scattering. Our analysis used charge densities described as a sum of spherical Bessel functions over a radius interval from zero to a cutoff of $R$ , with densities zero at larger radii. The fitting for the ground and $2^{+}$ states included constraints in the form of measured Barrett moments from muonic experiments and measured $B (E 2)$ transition rates from muonic and other experiments. Error bands were determined for the densities including statistical and normalization uncertainties, and model dependent uncertainties associated with contributions from higher terms in the spherical Bessel function form. We find that as neutrons are added from isotope to isotope, the charge is displaced from the region of 4.0 fm to the region of 7.5 fm. The rms radii of ${}^{144, 148, 150, 152}{Sm}$ were deduced with uncertainties of about 0.006 to 0.009 fm.

[NUCLEAR REACTIONS ${}^{144, 148, 150, 152}{Sm} (e, e^{'})$ analysis. Determination of charge and transition densities via Fourier-Bessel analysis.]

Precompound emission of light particles in the reaction ${}^{16}O$ + ${}^{238}U$ at 20 MeV/nucleon

T. C. Awes, G. Poggi, C. K. Gelbke, B. B. Back, B. G. Glagola, H. Breuer, and V. E. Viola, Jr.

Phys. Rev. C 24, 89 (1981) - Published 1 July, 1981

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Double differential cross sections have been measured for energetic $p$ , $d$ , $t$ , and $α$ particles emitted in reactions of 315 MeV ${}^{16}O$ ions on ${}^{238}U$ . In coincidence with light-particle emission, the momentum transfer to the target is determined by measuring the folding angle between the two fission fragments resulting from the sequential decay of the target nucleus. It is concluded that the emission of these particles occurs predominantly in fusionlike "central" collisions and at an early stage of the reaction. The energy and angular distributions are described by thermal emission from a source moving with approximately half of the beam velocity. Alternatively, the energy spectra can be explained by emission from a rotating hot spot. The cross sections for $d$ , $t$ , and $α$ emission can be described in terms of a generalized form of the coalescence model which takes into account the Coulomb repulsion from the target nucleus.

[NUCLEAR REACTIONS ${}^{238}U ({}^{16}O, X f)$ , $x = p, d, t, α$ , $E = 315$ MeV; measured $σ (E_{x}, θ_{x})$ and fission fragment folding angle distribution. Analysis in terms of hot spot, moving source, and coalescence models.]

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$σ$ model in the many-body problem

Exact multiple scattering theory of two-nucleus collisions including the Pauli principle

Isomeric and high-spin states of ${}^{94}{Tc}$ and the search for yrast isomers near $N \sim 50$

Beta-ray branching in the decay of ${}^{20}F$

Half-lives of ${}^{199}{Rn}$ and ${}^{199}{Rn}^{m}$

Analysis of $π^{0}$ photoproduction measurements near threshold on light nuclei

Surface coefficients of Skyrme-Orsay forces

Pion photoproduction on ${}^{27}{Al}$ : The effect of $V_{opt}$

Search for a fusion $L$ window in the ${}^{16}O$ + ${}^{16}O$ system at $E_{c . m .} = 34$ MeV

${\frac{1}{2}}^{+} \to {\frac{1}{2}}^{-}$ beta decay of ${}^{19}{Ne}$ and the parity nonconserving $NN$ force

Confirmation of the photoneutron cross section for ${}^{4}{He}$ below 33 MeV

Heavy ion resonances in mismatched channels

Erratum: Deuteron photodisintegration: Impulse approximation and gauge invariance

Alternative to Padé technique for solving scattering integral equations

Collective and neutron-structure effects in the elastic scattering of vector polarized deuterons in the $A = 90$ mass region

${}^{40}{Ca} (d, {}^{3}{He}) {}^{39}K$ reaction at 76 MeV

Coulomb wave expansion in electron scattering

Analysis of precompound processes in ( $p, n$ ) reactions with the statistical multistep direct emission theory

Charge and transition densities for the samarium isotopes by electron scattering

Precompound emission of light particles in the reaction ${}^{16}O$ + ${}^{238}U$ at 20 MeV/nucleon

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