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Selection rule for $E 1$ transitions

D. J. Millener

Phys. Rev. C 22, 1355(R) (1980) - Published 1 September, 1980

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Double-folding model potentials for ${}^{6}{Li}$ elastic scattering at 99 MeV

D. P. Stanley, F. Petrovich, and P. Schwandt

Phys. Rev. C 22, 1357(R) (1980) - Published 1 September, 1980

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Double-folding model potentials generated from a realistic nucleon-nucleon interaction and densities that are consistent with electron scattering are used to generate angular distributions for ${}^{6}{Li}$ elastic scattering at 99 MeV. When used to calculate observed angular distributions it is found that the double-folding model potential is roughly twice the potential required to generate a fit to the data. This is consistent with observations at both lower and higher ${}^{6}{Li}$ energies.

NUCLEAR REACTIONS ${}^{12}C$ , ${}^{28}{Si}$ , ${}^{40}{Ca}$ , ${}^{58}{Ni}$ , ${}^{90}{Zr}$ , ${}^{208}{Pb}$ ( ${}^{6}{Li}$ , ${}^{6}{Li}$ ), $E = 99$ MeV; calculated $σ (θ)$ with double-folding model potentials.

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$l_{crit}$ deduced from fragment angular distributions in ${}^{4}{He}$ -ion-induced fission

R. K. Choudhury, Rekha Govil, and S. S. Kapoor

Phys. Rev. C 22, 1360(R) (1980) - Published 1 September, 1980

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The published fragment anisotropy data in the fission of ${}^{209}{Bi}$ induced by 23-140 MeV ${}^{4}{He}$ ions are analyzed to deduce $l_{crit}$ for different bombarding energies. These values of $l_{crit}$ are found to be significantly lower than the optical model values of $l_{max}$ at higher bombarding energies. The theoretical values of $l_{crit}$ based on trajectory calculations with proximity potential and one body friction formalism are seen to agree with the experimentally deduced values. The significance of the above analysis for alternative experimental determination of ${}^{4}{He}$ ion fusion (compound nucleus formation) cross section through deduction of $l_{crit}$ is also pointed out.

NUCLEAR REACTIONS, FISSION $l_{crit}$ from fission fragment angular distributions; ${}^{209}{Bi}$ ( ${}^{4}{He}$ , $f$ ); $E_{α} = 23 - 140$ MeV.

RAPID COMMUNICATION

Generalized-master-equation theory for heavy ion collisions

R. K. Tripathi and L. Satpathy

Phys. Rev. C 22, 1363(R) (1980) - Published 1 September, 1980

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We apply nonequilibrium quantum statistical mechanics to the description of heavy ion collisions. Starting from the Liouville-Von Neumann equation we derive via the generalized master equation, the drift and diffusion coefficients.

NUCLEAR REACTIONS heavy ions nonequilibrium quantum statistical mechanics, drift and diffusion coefficients.

Ground-state ( $p, t$ ) cross sections for $sd$ -shell nuclei

N. Anantaraman

Phys. Rev. C 22, 945 (1980) - Published 1 September, 1980

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Ground-state ( $p, t$ ) cross sections measured for five $sd$ -shell nuclei are, with one exception, explained well by the shell-model calculations of Chung and Wildenthal. The deviation in the case of the ${}^{18}O (p, t) {}^{16}O$ reaction is quantitatively explained by taking account of the core-excited components in ${}^{16}O$ and ${}^{18}O$ .

NUCLEAR REACTIONS ${}^{18}O$ , ${}^{22}{Ne}$ , ${}^{26}{Mg}$ , ${}^{30}{Si}$ , ${}^{34}S (p, t)$ to ground states, $E_{p} = 23$ MeV, measured $σ (θ)$ , enriched targets. DWBA analysis; comparison with shell model.

Particle identity and the optical potential for elastic two-fragment collisions

R. Goldflam and K. L. Kowalski

Phys. Rev. C 22, 949 (1980) - Published 1 September, 1980

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The permutation symmetries resulting from particle identity are incorporated into a complete and consistent set of scattering integral equations which are partition labeled and which also possess a multiple scattering structure. These equations are applied to the investigation of the optical potential for elastic twofragment collisions including all identity effects. It is found that, among the standard off-shell extensions for the transition operators, only the one proposed by Alt, Grassberger, and Sandhas is entirely satisfactory for the definition of the optical potential. A dynamical integral equation for the symmetrized optical potential is derived. Several alternative forms of this equation are developed. Various low-order approximations to these equations are proposed.

NUCLEAR REACTIONS Connected-kernel $N$ -particle equations with multiple scattering structure including permutation symmetries. Dynamical equations for the optical potential for elastic collisions of two fragments composed of groups of identical particles.

Exact treatment of the Pauli principle in multiple scattering theory

S. A. Gurvitz

Phys. Rev. C 22, 964 (1980) - Published 1 September, 1980

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Exact equations for projectile-nucleus scattering are derived in which the effects of the Pauli principle are fully included. The resulting amplitude has two components; one resembles multiple scattering for distinguishable particles and the other describes distorted cluster exchange. The equations are simple to use and as such constitute an improvement over the present approximate schemes.

NUCLEAR REACTIONS Multiple scattering series, Pauli principle, cluster exchange, optical potential.

Deuteron photodisintegration: Impulse approximation and gauge invariance

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

Phys. Rev. C 22, 968 (1980) - Published 1 September, 1980

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We study the question of whether calculations of deuteron photodisintegration respect gauge invariance, and show that the impulse approximation is in severe disagreement with gauge invariance. The method in which Siegert's theorem is implemented is consistent with gauge invariance to within ten percent. We introduce a modification of the impulse approximation in which the current is conserved exactly. For deuteron photodisintegration this method yields essentially the same results as that of Partovi. Our method can easily be applied to electron- or neutrinonucleus scattering.

NUCLEAR REACTIONS ${}^{2}H (γ, p) n$ ; impulse approximation versus gauge invariance.

Failure of the connected-kernel method

V. V. Komarov, V. L. Shablov, A. M. Popova, and T. A. Osborn

Phys. Rev. C 22, 976 (1980) - Published 1 September, 1980

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The collision of two mutually interacting particles with a fixed force field is studied. In this problem it is shown that the widely used connected-kernel method encounters serious technical difficulties. We prove that if the mutual interaction between the particle pair is switched off then the coupled-component wave function equations characteristic of Faddeev's approach to the three-body problem do not have unique solutions. Specifically, it is shown that the homogeneous version of these equations have a nontrivial solution on the real energy axis. The technical criteria for defining this homogeneous solution is precisely that employed by Faddeev in his mathematical analysis of the three-body problem. In a similar fashion we show that the connected-kernel $t$ -matrix equations fail in that they do not manifestly display all the known singularity structure of the exact $t$ matrix. A reliable method for developing coupled-component $t$ -matrix equations based on the convolution representation of few-body Green's functions is described.

NUCLEAR REACTIONS Scattering theory. Inherent difficulties in the connected-kernel approach to the few-body collision problem. Convolution Green's functions and their use in resolving these difficulties.

Final state interaction in ( ${}^{3}{He}$ , ${}^{2}{He}$ ) reactions

T. V. Congedo, I. S. Lee-Fan, and B. L. Cohen

Phys. Rev. C 22, 985 (1980) - Published 1 September, 1980

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The two protons from ${}^{2}{He}$ breakup following ( ${}^{3}{He}$ , ${}^{2}{He}$ ) reactions were detected in coincidence, and energy and angular correlations between them were studied and compared with predictions of the final state interaction theories of Watson and Migdal and Phillips, Griffy, and Biedenharn. The angular correlation between the breakup protons drops off much faster than predicted by these theories; a final state interaction empirically derived to fit the angular correlation is sharply peaked at a breakup energy ≈ 0.6 MeV and is quite narrow. Energy distributions of the protons have a dip at the center for small correlation angles which disappears at larger angles. This is well predicted by all final state interaction theories but the slopes of these distributions are much better fit by the empirical final state interaction than by Watson and Migdal or by Phillips, Griffy, and Biedenharn. By maintaining a constant small correlation angle (proton detectors close together), ${}^{2}{He}$ angular distributions were measured and found to be in good agreement with distorted-wave Born approximation predictions.

NUCLEAR REACTIONS ${}^{64}{Ni} ({}^{3}{He}, 2 p)$ , $E = 13$ MeV; measured $σ (θ)$ , $pp$ correlation; deduced $pp$ FSI; calculated ${}^{2}{He}$ detection efficiency. ${}^{9}{Be} ({}^{3}{He}, 2 p)$ , $E = 13$ MeV; measured $σ (θ)$ . ${}^{27}{Al}$ , ${}^{90}{Zr} ({}^{3}{He}, 2 p)$ measured $pp$ correlation. ${}^{51}V$ , ${}^{65}{Cu}$ , ${}^{89}Y ({}^{3}{He}, 2 p)$ , $E = 13 MeV, 17 MeV$ , measured $σ (θ)$ , DWBA analysis.

${}^{189, 191}{Pt}$ via the ( $p, d$ ) reaction

J. Kalifa, G. Berrier-Ronsin, M. Vergnes, G. Rotbard, J. Vernotte, Y. Deschamps, and R. Seltz

Phys. Rev. C 22, 997 (1980) - Published 1 September, 1980

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The ( $p, d$ ) reaction has been performed at 25 MeV incident energy, on a rare ${}^{190}{Pt}$ target (35%) and on targets of ${}^{192}{Pt}$ (57%) and natural Pt. In ${}^{189}{Pt}$ , eleven levels are observed up to 600 keV. In ${}^{191}{Pt}$ , 18 levels are observed, four for the first time, up to 925 keV. Mass excesses are deduced for ${}^{191}{Pt}$ , ${}^{190}{Pt}$ , ${}^{189}{Pt}$ , and ${}^{188}{Pt}$ . Comparison of the experimental angular distributions with distorted-wave Born approximation calculations allows the determination of parity and spin limits for most of the final levels. Spectroscopic factors are deduced. Comparison with preceding experiments on heavier isotopes shows a smooth variation for the observed strengths between $A = 197$ and $A = 189$ , with a minimum fragmentation of the $l = 1$ strength in ${}^{193}{Pt}$ .

NUCLEAR REACTIONS ${}^{192, 190}{Pt} (p, d)$ , $E = 25$ MeV; ${}^{191, 190, 189, 188}{Pt}$ deduced mass excesses; measured $σ (θ)$ ; ${}^{191, 189}{Pt}$ deduced levels, $E$ , $J$ , $π$ , $S$ .

Expression of the half-off-shell quasiphases due to nonlocal interactions in terms of on-shell phase functions

T. Dolinszky

Phys. Rev. C 22, 345 (1980) - Published 1 August, 1980

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For local and nonlocal interactions, the standard method of solving an integral equation furnishes a set of half-off-shell quasiphases at the price of an integration in two and in three variables, respectively. For local interactions, the phase approach is known to supply a single quasiphase via a small number of integrations in a single variable each. The phase approach is generalized in this paper to cover the nonlocal case in treating quasiphases. A new quasiphase differential equation is derived. The explicit solution furnishes a single half-off-shell quasiphase at the expense of essentially an integration in two variables only.

NUCLEAR REACTIONS Scattering theory, off-shell phases versus on-shell phases.

Lifetime of the 1.04 MeV state in ${}^{18}F$

J. Keinonen, H. -B. Mak, P. Skensved, J. R. Leslie, and W. McLatchie

Phys. Rev. C 22, 351 (1980) - Published 1 August, 1980

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The lifetime of the 1.04 MeV ( $J^{π} = 0^{+}$ , $T = 1$ ) state in ${}^{18}F$ has been measured to be ${2.7}_{- 0.4}^{+ 0.6}$ fs using the Doppler shift attenuation method through the ${}^{18}O (p, n) {}^{18}F$ reaction. An ${}^{18}O$ target implanted into Ta was used in the measurement. Experimental correction factors for the nuclear and electronic stopping powers were used in the deduction of the lifetime. Based on the revised lifetime, the predicted circular polarization $P_{γ} (1.08 MeV)$ of the transition 1.08 MeV ( $0^{-}$ ,0) → 0 MeV ( $1^{+}$ ,0) is related to the parity nonconserving matrix element $〈 1.04 (0^{+}, 1) | V^{PNC} | 1.08 (0^{-}, 0) 〉$ by $P_{γ} (1.08 MeV) = \pm ({5.8}_{- 0.7}^{+ 0.5}) \times 10^{13} Me V^{- 1} 〈 1.04 (0^{+}, 1) | V^{PNC} | 1.08 (0^{-}, 0) 〉$ .

NUCLEAR REACTIONS ${}^{18}O (p, n) {}^{18}F$ , $E = 3.75$ MeV; measured Doppler-shift attenuation, ${}^{18}F$ 1042-keV level; deduced $τ_{m}$ . Implanted target.

First two members of the $K^{π} = 0^{-}$ band in ${}^{20}{Ne}$

J. D. MacArthur, H. C. Evans, J. R. Leslie, and H. -B. Mak

Phys. Rev. C 22, 356 (1980) - Published 1 August, 1980

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In an alpha capture experiment on an ${}^{16}O$ gas target, the $3^{-}$ , 7.156 MeV state in ${}^{20}{Ne}$ has been observed to decay to the $1^{-}$ , 5.782 MeV and the $4^{+}$ , 4.248 MeV states with gamma ray branches of 45 ± 5% and 55 ± 5%, respectively. The strengths of the 1374 and 2908 keV transitions were deduced to be $B (E 2) = 51 \pm 8$ W.u. and $B (E 1) = 79 \pm 9$ μ W.u., respectively. The strongly enhanced $E 2$ rate for the $3^{-}$ to $1^{-}$ transition is convincing evidence for these two states being the first members of this $K^{π} = 0^{-}$ band in ${}^{20}{Ne}$ . From resonance scattering experiments, the alpha widths for these two states were determined to be 28 ± 3 eV and 8.1 ± 0.3 keV, respectively; values in agreement with cluster calculations of alpha widths in ${}^{20}{Ne}$ .

NUCLEAR REACTIONS Measured $σ (E, θ)$ for ${}^{16}O (α, α) {}^{16}O$ and $σ (E_{R})$ for ${}^{16}O (α, γ) {}^{20}{Ne}$ ; deduced $Γ_{α}$ for $E_{x} = 5.782 and 7.156$ MeV and radiative transition rates from $E_{x} = 7.156$ MeV.

Unitary content of the optical potential for an uncorrelated target

David M. Schneider

Phys. Rev. C 22, 362 (1980) - Published 1 August, 1980

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The optical potential for an uncorrelated target is derived. Operator identities are used to obtain the partial cross sections to all reactive channels in this model. Using a set of approximations, the optical potential is written in first-order form. The partial cross sections to all channels implied by the first-order potential can be written as a generalization of the usual distorted wave impulse approximation. Under certain assumptions a sum rule is obtained. The high energy limit of our results are then examined by the use of Glauber's theory.

NUCLEAR REACTIONS First-order optical potential, reactive content, DWIA, local field correction, Glauber theory.

Inelastic electron scattering from ${}^{29}{Si}$

K. E. Whitner, C. F. Williamson, B. E. Norum, and S. Kowalski

Phys. Rev. C 22, 374 (1980) - Published 1 August, 1980

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Electron scattering from ${}^{28}{Si}$ and ${}^{29}{Si}$ has been performed at energies from 126 to 293 MeV and at angles of 45° and 90°. Form factors were extracted for levels below 5.0 MeV in ${}^{28}{Si}$ and ${}^{29}{Si}$ over an effective momentum transfer range of 0.6 to 2.1 ${fm}^{- 1}$ . A particle-phonon coupling calculation using harmonic-oscillator single-particle states and data from ${}^{28}{Si}$ give a reasonable description of the low-lying states of ${}^{29}{Si}$ .

NUCLEAR REACTIONS ${}^{28}{Si} (e, e^{'})$ first 2 excited states; ${}^{29}{Si} (e, e^{'})$ first 5 excited states; measured form factors 45° and 90°, $0.6 <~ q <~ 2.1$ ${fm}^{- 1}$ ; natural Si target; PWBA analysis, vibrating core and intermediate coupling for ${}^{29}{Si}$ .

Neutron total cross section for tritium

T. W. Phillips, B. L. Berman, and J. D. Seagrave

Phys. Rev. C 22, 384 (1980) - Published 1 August, 1980

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The neutron total cross sections for hydrogen, deuterium, and tritium have been measured with the neutron-time-of-flight technique. The tritium data span the neutron energy range from 60 keV to 80 MeV, with an overall systematic uncertainty which varies from 0.5% for energies below 17 MeV to 2% at the highest energy measured; the statistical uncertainties exceed these values only below 200 keV and above 7 MeV. The three-mole high-pressure gas samples were nearly isotopically pure. Excellent agreement is found with accepted cross sections for hydrogen and deuterium, and with previous Van de Graaff measurements for tritium except at the lowest-energy point at 290 keV. A minimum in the cross section near 600 keV (with a rise at lower energy) is newly observed. The cross section in the heretofore unexplored energy region between 7 and 14 MeV exhibits no structure, and thus no evidence for the existence of a bound fourneutron state. The extrapolated zero-energy cross section is found to be 1.70±0.03 b, in sharp disagreement with previous thermal-energy observations, but in agreement with calculations which also yield the currently accepted coherent scattering length 3.73 fm. Agreement with a prediction from an analysis of $p$ - ${}^{3}{He}$ data is within 1% at the resonance peak near 3.5 MeV, but the data differ from this prediction by as much as 6% at lower and higher energies. Thus, within the framework of a suitable theoretical analysis, the present data might provide a measure of the departure from charge symmetry of the nuclear force.

NUCLEAR REACTIONS Measured $σ (E_{n})$ for ${}^{1}H$ , ${}^{2}H$ , 0.06-80 MeV; LINAC, NTOF technique, isotopic, high-pressure gas samples; tritium; four-nucleon system; four-neutron state; scattering length; charge symmetry; $R$ matrix.

Polarized proton capture on ${}^{30}{Si}$

C. P. Cameron, R. D. Ledford, M. Potokar, D. G. Rickel, N. R. Roberson, H. R. Weller, and D. R. Tilley

Phys. Rev. C 22, 397 (1980) - Published 1 August, 1980

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The 90° yield curves for the ${}^{30}{Si} (p, γ_{0}) {}^{31}P$ and ${}^{30}{Si} (p, γ_{1}) {}^{31}P$ reactions have been measured for $E_{p} = 5.0 to 28.0$ MeV. Angular distributions of cross section and analyzing power were obtained at twelve energies between $E_{p} = 6.36 and 14.45$ MeV. The cross sections were measured at nine angles between 30° and 154°, the analyzing power at seven angles between 42° and 142°. For the case of ( $\vec{p}, γ_{0}$ ) the complex $T$ -matrix elements were extracted, assuming that the angular distributions are governed by coherent $E 1$ and $E 2$ processes. Two $σ (E 2)$ yield curves are obtained, one of which exhausts 9-12% of the $Δ T = 0$ $E 2$ energy weighted sum rule while the other exhausts 21-31%. The results are compared to direct-semidirect model calculations which suggest that the larger $E 2$ cross sections are the physical solutions.

NUCLEAR REACTIONS ${}^{30}{Si} (\vec{p}, γ_{0})$ ${}^{30}{Si} (\vec{p}, γ_{1})$ measured $σ (θ)$ and $A (θ)$ , $E_{p} = 6.4 to 15.0$ MeV. ${}^{30}{Si} (p, γ_{0})$ ${}^{30}{Si} (p, γ_{1})$ measured $σ (90 °)$ , $E_{p} = 5.0 to 28.0$ MeV. Deduced $E 1$ and $E 2$ $T$ -matrix amplitudes and phases. Compared to model calculations.

( $d$ , ${}^{6}{Li}$ ) reaction on ${}^{24}{Mg}$ and ${}^{26}{Mg}$ at $E_{d} = 80$ MeV

W. Oelert, W. Chung, A. Djaloeis, C. Mayer-Böricke, and P. Turek

Phys. Rev. C 22, 408 (1980) - Published 1 August, 1980

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The ( $d$ , ${}^{6}{Li}$ ) reaction on ${}^{24}{Mg}$ and ${}^{26}{Mg}$ has been measured at a bombarding energy of 80 MeV. Angular distributions were obtained in an angular range of 6° (2° for the ground state transitions) to 35° lab. Experimentally an excitation energy range up to 30 MeV was observed. In the framework of finite-range distorted-wave Born approximation calculations $α$ spectroscopic factors were extracted and compared to recent shell-model predictions.

NUCLEAR REACTIONS ${}^{24}{Mg} (d, {}^{6}{Li}) {}^{20}{Ne}$ , ${}^{26}{Mg} (d, {}^{6}{Li}) {}^{22}{Ne}$ . $E_{d} = 80$ MeV, measured $σ (E_{{}^{6}{Li}}, θ)$ . Enriched targets. Finite-range DWBA calculations. Deduced alpha spectroscopic factors.

Baer-Kouri-Levin-Tobocman and Faddeev equations for the three-body problem with pairwise interactions

Donald J. Kouri

Phys. Rev. C 22, 422 (1980) - Published 1 August, 1980

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We reanalyze the Baer-Kouri-Levin-Tobocman and Faddeev equations for the three-body problem with pairwise interactions. The approach to the Bear-Kouri-Levin-Tobocman equations is more in the spirit of the usual Faddeev equations. The detailed operators which appear as "effective interactions" are different from those appearing in earlier forms of the Faddeev equations. It is shown that the same effective interactions appear in both the Baer-Kouri-Levin-Tobocman and Faddeev-type equations. The resulting form of the Baer-Kouri-Levin-Tobocman equations may be more suitable for the approximate treatment of breakup effects than previous forms of these equations.

NUCLEAR REACTIONS Scattering theory Baer-Kouri-Levin-Tobocman three-body scattering equations, Faddeev three-body scattering equations, three-body scattering with pairwise interactions.

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Selection rule for $E 1$ transitions

Double-folding model potentials for ${}^{6}{Li}$ elastic scattering at 99 MeV

$l_{crit}$ deduced from fragment angular distributions in ${}^{4}{He}$ -ion-induced fission

Generalized-master-equation theory for heavy ion collisions

Ground-state ( $p, t$ ) cross sections for $sd$ -shell nuclei

Particle identity and the optical potential for elastic two-fragment collisions

Exact treatment of the Pauli principle in multiple scattering theory

Deuteron photodisintegration: Impulse approximation and gauge invariance

Failure of the connected-kernel method

Final state interaction in ( ${}^{3}{He}$ , ${}^{2}{He}$ ) reactions

${}^{189, 191}{Pt}$ via the ( $p, d$ ) reaction

Expression of the half-off-shell quasiphases due to nonlocal interactions in terms of on-shell phase functions

Lifetime of the 1.04 MeV state in ${}^{18}F$

First two members of the $K^{π} = 0^{-}$ band in ${}^{20}{Ne}$

Unitary content of the optical potential for an uncorrelated target

Inelastic electron scattering from ${}^{29}{Si}$

Neutron total cross section for tritium

Polarized proton capture on ${}^{30}{Si}$

( $d$ , ${}^{6}{Li}$ ) reaction on ${}^{24}{Mg}$ and ${}^{26}{Mg}$ at $E_{d} = 80$ MeV

Baer-Kouri-Levin-Tobocman and Faddeev equations for the three-body problem with pairwise interactions

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