Standard Optical Potential Research Articles

Optical lattice for a tripodlike atomic level structure

Standard optical potentials use off-resonant laser standing wave induced AC-Stark shift. In a recent development [Phys. Rev. Lett. {\bf 117}, 233001 (2016)] a three-level scheme in $\Lambda$ configuration coupled coherently by resonant laser fields was introduced leading to an effective lattice with subwavelength potential peaks. Here as an extension of that work to a four level atomic setup in the tripod configuration is used to create spin $1/2$-like two-dimensional dark-space with 1D motion and the presence of external gauge fields. Most interestingly for a possible application, the lifetime for a dark subspace motion is up to two orders of magnitude larger than for a similar $\Lambda$ system. The model is quite flexible leading to lattices with significant nearest, next-nearest, or next-next-nearest hopping rates, $J_1,J_2,J_3$ opening up new intriguing possibilities to study, e.g. frustrated systems. The characteristic Wannier functions lead also to new type of inter-site interactions not realizable in typical optical lattices.

Nuclear physics uncertainties of the astrophysical γ-process studied through the 64Zn(p,α)61Cu and 64Zn(p,γ)65Ga reactions

In a recent work, the cross section measurement of the 64Zn(p,α)61Cu reaction was used to prove that the standard α-nucleus optical potentials used in astrophysical network calculation fail to reproduce the experimental data at energies relevant for heavy element nucleosynthesis. In the present paper the analysis of the obtained experimental data are continued by comparing the results with the predictions using different parameters. It is shown that the recently suggested modification of the standard optical potential leads to a better description of the data.

Reduction of fusion and reaction cross sections at near-barrier energies

We investigate three of the most frequently used methods to reduce fusion and total reaction excitation functions. For this purpose, we apply them in two situations. First, we consider theoretical cross sections obtained by single-channel calculations based on standard optical potentials. In this case, the cross sections are not influenced by any particular nuclear property. Thus, the method is successful if the cross sections for different systems are about the same. In the case of fusion excitation functions, we found that the fusion function method works very well, being much better than the other two methods. Regarding total reaction excitation functions, none of the methods is satisfactory. Their reduced reaction cross sections maintain a strong dependence on the atomic and mass numbers of the collision partners. However, they perform reasonably well when compared to similar systems. Next, we use the three methods to reduce experimental fusion and reaction cross sections for many systems, over a broad mass range. Our conclusions are consistent with the ones reached for our theoretical cross sections, resulting from single-channel calculations. That is, the fusion function method is the best for fusion data, whereas none of the three methods works for total reaction.

α-induced cross sections ofCd106for the astrophysicalpprocess

The 106Cd(alpha,gamma)110Sn reaction cross section has been measured in the energy range of the Gamow window for the astrophysical p-process scenario. The cross sections for 106Cd(alpha,n)109Sn and for 106Cd(alpha,p)109In below the (alpha,n) threshold have also been determined. The results are compared with predictions of the statistical model code NON-SMOKER using different input parameters. The comparison shows that a discrepancy for 106Cd(alpha,gamma)110Sn when using the standard optical potentials can be removed with a different alpha+106Cd potential. Some astrophysical implications are discussed.

Pauli blocking effects for nucleon-nucleus scattering.

Theoretical predictions for nucleon-nucleus scattering are customarily based on multiple-scattering formalisms in which the projectile-nucleon--struck-target-nucleon two-body subsystem is antisymmetrized and in which the target wave function is antisymmetric with respect to the nucleon constituents. Although formalisms exist for nucleon-nucleus scattering which account for full ([ital A]+1)-body antisymmetrization, these theories have not been adequately implemented in numerical applications. Pauli blocking of the struck target nucleon in intermediate scattering states is implicitly included in standard optical potential calculations which consistently include terms through second-order in the projectile-target nucleon scattering [ital t] matrix. In this work the multiple scattering expansion of the fully antisymmetrized nucleon-nucleus optical potential is organized so as to make explicit corrections to the standard optical potential due to Pauli blocking of the projectile nucleon in intermediate scattering states. Numerical calculations are presented for the resulting density dependent, projectile-target nucleon effective interaction and comparison with a previous density dependent model is given. It is shown that density dependent effective interaction [ital t] matrices for nucleon-nucleus scattering calculations should include Pauli blocking of just the projectile nucleon and binding potential corrections for just the target nucleon.

A study of the strong interaction effects on pionic 3d and 4f levels in 181Ta, natRe, natPt, 197Au, 208Pb, 209Bi and 237Np

The pionic X-ray spectra of 181Ta, natRe, natPt, 197Au, 208Pb, 209Bi and 237Np have been investigated to obtain data for a systematical study of the pionic 3d and 4f levels. In order to reduce background the experimental method has been improved by using an array of Compton suppression BGO-shields and neutron time-of-flight discrimination. The widths of the pionic 3d levels are observed to be narrower by a factor 1.5 than theoretical predictions obtained with standard optical potentials. A deviation is also found for the strong interaction quadrupole shift, ϵ 2, for both the 4f and 3d orbits. A possible explanation for the smaller width, Γ 0(3 d), can be found by extending the parametrization of the optical potential with absorption terms.

An improved parametrization of the optical potential for pionic atoms

We try to find an improved phenomenological optical potential for pionic atoms in two steps. First, we perform a new fit of the parameters in the standard optical potentials by using a large data base of 140 pionic atom data. A χ 2 is obtained that is substantially lower than with any previous parameter set. In a second step, we extend the number of parameters by using a more general form for the terms quadratic in the nuclear density. This extended version yields a reduction of the χ 2 by about a factor of two. The new fit includes a good description of shifts and widths of the deeply bound 3d orbits in heavy nuclei such as 181Ta, natRe, natPt, 197Au, 208Pb and 209Bi. The value of the additional parameters in the extended version are difficult to interpret in the context of the chosen form of the optical potential and indicate that higher-order effects play a role.

Deeply bound 1s and 2p states in pionic atoms

New results were obtained on pionic 1s levels in 24Mg, 27Al and 28Si, on 2p states in 93Nb and natRu, as well as on 3d states in 93Nb, natRu, natAg and natCd. For the first time the predicted repulsive shifts for the pionic 2p level have been observed. The following values were obtained for the strong-interaction shifts and widths (all values in keV); 24Mg: ε 1s 0 = −80.5 ± 0.6 and Γ 1s 0 = 24.3 ± 1.6; 27Al: ε 1s 0 = −115.5 ± 1.4 and Γ 1s 0 = 28.8 ± 1.2, 28Si: ε 1s 0 = −131.6 ± 2.0 and Γ 1s 0 = 41 ± 4; 93Nb: ε 2p 0 = −11 ± 3, Γ 2p 0 = 64 ± 8, ε 3d 0 = 0.74 ± 0.02 and Γ 3d 0 = 0.402 ± 0.016; natRu: ε 2p 0 = −48 ± 7, Γ 2p 0 = 77 ± 24, ε 3d 0 = 1.39 ± 0.08 and Γ 3d 0 = 0.75 ± 0.08; natAg: ε 3d 0 = 1.94 ± 0.07 and Γ 3d 0 = 1.44 ± 0.05 and natCd: ε 3d 0 = 2.14 ± 0.09 and Γ 3d 0 = 1.65 ± 0.07. The results are in reasonable agreement with the predictions of the standard optical potentials.

Suppression of high intermediate momenta in the π-nucleus interaction

A new way of dealing with the unwanted high momentum components in low energy pion-nucleus optical potentials is presented. The method is developed strictly in accordance with a principle of “smoothness” which has been found very helpful in other contexts of nuclear physics. The effect of taking a standard optical potential and “smoothing” it is small for the pion elastic scattering cross section but large for the pion wavefunction in the nuclear interior. This has the dramatic and much needed effect of lowering the (p,π) differential cross section by an order of magnitude because this reaction is sensitive to the high momentum components of the wavefunction.

Photoproduction of strangeness in nuclei

The excitation of hypernuclei through kaon photoproduction is investigated in a Relativistic Impulse Approximation (RIA) framework. The elementary photoproduction amplitude is evaluated using diagrammatic techniques and includes low-lying hadron resonances whose coupling constants have been fitted to the data. The nuclear matrix elements are calculated in momentum space to include Fermi motion and nonlocalities in the production operator. The nucleon and hyperon bound state wavefunctions are obtained by solving the Dirac equation with scalar and vector potentials. Kaon distortion is included via a standard optical potential. Relativistic effects are found to be important along with the effects of nonlocalities, whereas kaon distortion is of minor significance.

Anomalous strong interaction shifts and widths of the 3d state in pionic Pt and Au

The poinic 4f → 3d X-ray transitions in Pt and Au have been observed. The strong interaction monopole shifts ϵ o and widths Γ o of the 4f and 3dd levels have been deduced. For the pionic 4f levels standard optical potentials predict the experimental values quite well, whereas the deeper bound 3d states have shifts and widths that are smaller by a factor of about two than the theoretical predictions.

Pionic 4f → 3d transition in 181Ta, natural Re, and 209Bi And the strong interaction level shift and width of the pionic 3d state

Owing to a powerful Compton-suppression technique it was possible to observe for the first time the pionic 4f → 3d X-ray transition in elements heavier than A = 150. The strong interaction monopole shifts ε 0 and widths Γ 0 as well as the quadrupole splitting of the 3d levels have been measured in Ta, Re and Bi. Thus in addition to the strongly shifted and broadened 5g → 4f transitions, a second, strongly affected line is available for these elements. For the pionic 4f levels, standard optical potentials fit the strong interaction shifts and broadenings quite well. The now observed, deeper-lying 3d states in Ta, Re and Bi have shifts and widths that differ by a factor of 2 or more from the standard optical potential predictions. From the observed relative X-ray intensities of the pionic cascade we also extract the strong interaction widths of the 5g and 4f levels.

Observation of the E2 nuclear resonance effect in some pionic atoms

The E2 nuclear resonance effect has been studied in the pionic atoms of 48Ti, 104Ru, 110Pd, 111, 112Cd, and 150Sm. For pionic 111, 112Cd, where the “mixed-in” level is directly observable, the measured effect agrees very well with theory. For pionic 110Pd, the measurement confirms for the first time the prediction of Ericson et al. that the P-wave π-nucleus interaction becomes repulsive for large enough Z, but also implies a P-wave absorptive width smaller than predicted by standard optical potentials. The experimental results for 104Ru and 150Sm agree with simple theoretical model, while that for 48Ti does not.

Scattering of 10.4 MeV polarized neutrons from bismuth and lead between 2° and 65°

The polarization and differential cross sections for the scattering of 10.4 MeV neutrons from lead and bismuth are measured from 1.5\ifmmode^\circ\else\textdegree\fi{} to 65\ifmmode^\circ\else\textdegree\fi{}. No significant differences are found between the polarizations in the scattering at small angles in contrast to the situation reported at 2.45 MeV. The data over the complete angular range are reproduced using a standard optical potential with the addition of the long-range interaction between the neutron magnetic moment and the nuclear Coulomb field.

Back-angle anomalies in alpha scattering: Inelastic scattering from the calcium isotopes

Cross sections for elastic and inelastic $\ensuremath{\alpha}$ scattering on $^{40,42,44,48}\mathrm{Ca}$ have been measured to several excited states. The bombarding energy (lab) is 24 MeV for $\ensuremath{\alpha}$ +$^{40,42,44}\mathrm{Ca}$ and is 24 and 29 MeV for $\ensuremath{\alpha}$ +$^{48}\mathrm{Ca}$. Particular emphasis is given to the back-angle data. In addition to the anomaly of $\ensuremath{\alpha}$ +$^{40}\mathrm{Ca}$ elastic scattering at backward angles previously reported by many workers anomalous features are also observed in inelastic scattering. It is found that the backward anomaly of the $\ensuremath{\alpha}$ +$^{40}\mathrm{Ca}$ inelastic cross sections is strongest for the ${0}^{+}$ states and gradually decreases with increasing spins of the final states (${1}^{\ensuremath{-}}$, ${3}^{\ensuremath{-}}$, ${5}^{\ensuremath{-}}$). The only exception is the scattering to the ${2}^{+}$ state at 3.90 MeV, for which the cross sections exhibit a regular decrease toward backward angles. The inelastic cross sections for the $^{42,44,48}\mathrm{Ca}$ isotopes are generally smaller at backward angles as compared to those for $^{40}\mathrm{Ca}$. In general, the observed anomalies for inelastic scattering at back angles are in close analogy to those known for elastic scattering. An interpretation of the data and of the anomalies in terms of coupled channels is given. Both a standard optical potential and one with an angular-momentum-dependent absorption have been used in the calculations. It is found that the large differences in the cross sections at backward angles, depending on the isotope and on the spin of the residual state, can be reproduced by coupled-channel calculations when an angular-momentum-dependent absorption in the optical potential is assumed.NUCLEAR REACTIONS $^{40,42,44,48}\mathrm{Ca}(\ensuremath{\alpha}, {\ensuremath{\alpha}}_{0})$, $^{40,42,44,48}\mathrm{Ca}(\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}})$, $E=24\ensuremath{-}29$ MeV; measured $\ensuremath{\sigma}(E, \ensuremath{\theta})$; deduced coupled-channel parameters. Enriched targets; $\ensuremath{\theta}=12.5\ensuremath{-}177.5\ifmmode^\circ\else\textdegree\fi{}$, $\ensuremath{\Delta}\ensuremath{\theta}=2.5\ifmmode^\circ\else\textdegree\fi{}$; calculated $\ensuremath{\sigma}(\ensuremath{\theta})$.

Corrections to the closure approximation for the optical potential

Target closure is a basic assumption made at the outset of many derivation of the standard optical potential. Using the formalism of Foldy and Walecka we show how the target dynamics, neglected in the closure approximation, can be incorporated into the scattering amplitude and the optical potential. To illustrate this procedure and to examine the nature of the nuclear effects, we evaluate the leading correction to the closure approximation by using a Fermi gas model for the nucleus. This simple picture is known to reproduce the major part of the nuclear response surface as observed in inelastic electron scattering.

Elastic scattering of 11.6 MeV vector polarized deuterons by 14N, 16O, 20Ne and 22Ne

The vector analysing power iT 11 of the elastic scattering of 11.6 MeV polarized deuterons by 14N, 16O, 20Ne and 22Ne and the corresponding differential cross section for the latter two nuclei have been measured and analysed in terms of a standard optical potential. The optical model was found to provide a reasonable description of the experimental data. The volume integral of the real central potential was used to compare various parameters sets obtained.

Elastic scattering of vector polarized deuterons from 48Ti, 49Ti, 50Ti, 51V, 52Cr

The elastic scattering of vector polarized deuterons with a mid-target energy of E d = 11.9 MeV from 48Ti, 49Ti, 50Ti, 51V and 52Cr was measured and analysed in terms of a standard optical potential containing a spin-orbit term. The analysis showed that all nuclei under investigation have very similar parameters. The depth, range and diffuseness of the Thomas-type spin-orbit potential tended to be small, typical values being V s.o. = 5.06 MeV, r s.o. = 0.70 fm, a s.o. = 0.40 fm ( 50 Ti) . A comparison of the results for target nuclei with spin ( 49Ti, 51V) to those for the neighbouring spin-zero nuclei yielded no hint for a target spindependent interaction.

Extension of the Optical Model and Its Application to the Elastic Scattering ofO16byO16Nuclei

The absorptive part of the optical potential is considered as a function of conserved quantum numbers such as the total angular momentum $J$. This investigation results in the introduction of a smooth cutoff in the strength of the absorptive potential as $J$ gets larger than a certain critical value. This value is typical of nonelastic channels, and the cutoff reflects poor matching between the angular momenta in the elastic channel and those in the nonelastic channels. Brief consideration is also given to other conserved or approximately conserved quantum numbers such as isobaric spin and parity. The standard optical potential is modified to include an angular-momentum dependence with a suitable cutoff, and is applied to the elastic scattering of $^{16}\mathrm{O}$ by $^{16}\mathrm{O}$ nuclei. In the energy range 15-36 MeV (c.m.), such an extended optical model gives a good description of all the gross features of the $^{16}\mathrm{O}$-$^{16}\mathrm{O}$ data. A repulsive core in the $^{16}\mathrm{O}$-$^{16}\mathrm{O}$ potential has been considered, but no definite evidence for it is found in the present analysis.