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We present STAR measurements of strange hadron (KS0, Λ, Λ¯, Ξ−, Ξ¯+, Ω−, Ω¯+, and ϕ) production at midrapidity (|y

Author(s): Adam, J; Adamczyk, L; Adams, JR; Adkins, JK; Agakishiev, G; Aggarwal, MM; Ahammed, Z; Alekseev, I; Anderson, DM; Aparin, A; Aschenauer, EC; Ashraf, MU; Atetalla, FG; Attri, A; Averichev, GS; Bairathi, V; Barish, K; Behera, A; Bellwied, R; Bhasin, A; Bielcik, J; Bielcikova, J; Bland, LC; Bordyuzhin, IG; Brandenburg, JD; Brandin, AV; Butterworth, J; Caines, H; Calderon De La Barca Sanchez, M; Cebra, D; Chakaberia, I; Chaloupka, P; Chan, BK; Chang, FH; Chang, Z; Chankova-Bunzarova, N; Chatterjee, A; Chen, D; Chen, JH; Chen, X; Chen, Z; Cheng, J; Cherney, M; Chevalier, M; Choudhury, S; Christie, W; Crawford, HJ; Csanad, M; Daugherity, M; Dedovich, TG; Deppner, IM; Derevschikov, AA; Didenko, L; Dong, X; Drachenberg, JL; Dunlop, JC; Edmonds, T; Elsey, N; Engelage, J; Eppley, G; Esha, R; Esumi, S; Evdokimov, O; Ewigleben, A; Eyser, O; Fatemi, R; Fazio, S; Federic, P; Fedorisin, J; Feng, CJ; Feng, Y; Filip, P; Finch, E; Fisyak, Y; Francisco, A; Fulek, L; Gagliardi, CA; Galatyuk, T; Geurts, F; Gibson, A; Gopal, K; Grosnick, D; Guryn, W; Hamad, AI; Hamed, A | Abstract: Particle production sensitive to nonfactorizable and nonperturbative processes that contribute to the underlying event associated with a high transverse momentum (pT) jet in proton+proton collisions at s=200 GeV is studied with the STAR detector. Each event is divided into three regions based on the azimuthal angle with respect to the highest-pT jet direction: In the leading jet direction ("Toward"), opposite to the leading jet ("Away"), and perpendicular to the leading jet ("Transverse"). In the Transverse region, the average charged particle density is found to be between 0.4 and 0.6 and the mean transverse momentum

We report new STAR measurements of the single-spin asymmetries $A_L$ for $W^+$ and $W^-$ bosons produced in polarized proton--proton collisions at $\sqrt{s}$ = 510 GeV as a function of the decay-positron and decay-electron pseudorapidity. The data were obtained in 2013 and correspond to an integrated luminosity of 250 pb$^{-1}$. The results are combined with previous results obtained with 86 pb$^{-1}$. A comparison with theoretical expectations based on polarized lepton-nucleon deep-inelastic scattering and prior polarized proton--proton data suggests a difference between the $\bar{u}$ and $\bar{d}$ quark helicity distributions for $0.05 < x < 0.25$. In addition, we report new results for the double-spin asymmetries $A_{LL}$ for $W^\pm$, as well as $A_L$ for $Z/\gamma^*$ production and subsequent decay into electron--positron pairs.

Author(s): Adam, J; Adamczyk, L; Adams, JR; Adkins, JK; Agakishiev, G; Aggarwal, MM; Ahammed, Z; Alekseev, I; Anderson, DM; Aoyama, R; Aparin, A; Arkhipkin, D; Aschenauer, EC; Ashraf, MU; Atetalla, F; Attri, A; Averichev, GS; Bairathi, V; Barish, K; Bassill, AJ; Behera, A; Bellwied, R; Bhasin, A; Bhati, AK; Bielcik, J; Bielcikova, J; Bland, LC; Bordyuzhin, IG; Brandenburg, JD; Brandin, AV; Bryslawskyj, J; Bunzarov, I; Butterworth, J; Caines, H; Calderon De La Barca Sanchez, M; Cebra, D; Chakaberia, I; Chaloupka, P; Chan, BK; Chang, FH; Chang, Z; Chankova-Bunzarova, N; Chatterjee, A; Chattopadhyay, S; Chen, JH; Chen, X; Cheng, J; Cherney, M; Christie, W; Crawford, HJ; Csanad, M; Das, S; Dedovich, TG; Deppner, IM; Derevschikov, AA; Didenko, L; Dilks, C; Dong, X; Drachenberg, JL; Dunlop, JC; Edmonds, T; Elsey, N; Engelage, J; Eppley, G; Esha, R; Esumi, S; Evdokimov, O; Ewigleben, J; Eyser, O; Fatemi, R; Fazio, S; Federic, P; Fedorisin, J; Feng, Y; Filip, P; Finch, E; Fisyak, Y; Fulek, L; Gagliardi, CA; Galatyuk, T; Geurts, F; Gibson, A; Grosnick, D; Gupta, A; Guryn, W | Abstract: We report the energy dependence of mid-rapidity (anti-)deuteron production in Au+Au collisions at sNN=7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV, measured by the STAR experiment at the BNL Relativistic Heavy Ion Collider. The yield of deuterons is found to be well described by the thermal model. The collision energy, centrality, and transverse momentum dependence of the coalescence parameter B2 are discussed. We find that the values of B2 for antideuterons are systematically lower than those for deuterons, indicating that the correlation volume of antibaryons is larger than that of baryons at sNN from 19.6 to 39 GeV. In addition, values of B2 are found to vary with collision energy and show a broad minimum around sNN=20-40 GeV, which might imply a change of the equation of state of the medium in these collisions.

The azimuthal anisotropic flow of identified and unidentified charged particles has been systematically studied in Cu+Au collisions at sNN=200 GeV for harmonics n=1–4 in the pseudorapidity range |η

Global polarization of $\Lambda$ hyperons has been measured to be of the order of a few tenths of a percent in Au+Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV, with no significant difference between $\Lambda$ and $\bar{\Lambda}$. These new results reveal the collision energy dependence of the global polarization together with the results previously observed at $\sqrt{s_{_{NN}}}$ = 7.7 -- 62.4 GeV and indicate noticeable vorticity of the medium created in non-central heavy-ion collisions at the highest RHIC collision energy. The signal is in rough quantitative agreement with the theoretical predictions from a hydrodynamic model and from the AMPT (A Multi-Phase Transport) model. The polarization is larger in more peripheral collisions, and depends weakly on the hyperon's transverse momentum and pseudorapidity $\eta^H$ within $|\eta^H

A new prototype of a Long-Strip Multi-Gap Resistive Plate Chamber (LMRPC) for the STAR Muon Telescope Detector (MTD) at RHIC has been developed. This prototype has an active area of 52 x 90 cm(2) and consists of six 250 mu m wide gaps. Each detector has 12 strips, read-out at both ends, which are each 3.8 cm wide and 90 cm long with 0.6 cm intervals. In cosmic-ray tests, the efficiency was larger than 95% and the time resolution was similar to 75 ps for the 94% Freon, 5% iso-butane, and 1% SF6 gas mixture. There was good uniformity in the performance across the different strips. The module was also tested in a proton beam at IHEP in Beijing. The efficiency was close to 100% and the best timing resolution achieved was 55 ps for the 90% Freon, 5% iso-butane, and 5% SF6 gas mixture. Trigger scans along and across the strip direction were also performed. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.

The STAR Collaboration has studied the pseudorapidity ( η ) elongated two-particle correlation structure known as the “ridge” since the first RHIC run. This ridge-like feature is observed in two-particle correlations with and without a selected tag, or trigger particle. Un-triggered correlations reveal the ridge structure in minimum-bias Cu–Cu and Au–Au collisions at s N N = 62 and 200 GeV. Accompanying this same-side (relative azimuth π / 2 ) ridge is an away-side ridge on η . Both the same- and away-side structures have corresponding correlation peaks in two-dimensional transverse momentum ( p t ) space. The p t and event-plane dependences of the same-side correlation structures have also been studied. A summary of the present experimental information and a discussion of the constraints which this body of data imposes on possible theoretical explanations of the ridge phenomenon are presented.

The inner tracking detector of the STAR experiment at the BNL Relativistic Heavy Ion Collider will consist of a three layer barrel structure of 216 silicon drift detectors. Calculations of the two-hit resolution achievable for these detectors are presented in this article. The effects on two-hit resolution of the electronic's response function, frequency of signal digitization and noise level are discussed.

Pion-nucleus elastic scattering at energies above the {Delta}(1232) resonance is studied using both {pi}{sup +} and {pi}{sup {minus}} beams on {sup 12}C, {sup 40}Ca, {sup 90}Zr, and {sup 208}Pb. The present data provide an opportunity to study the interaction of pions with nuclei at energies where second-order corrections to impulse approximation calculations should be small. The results are compared with other data sets at similar energies and with four different first-order impulse approximation calculations. Significant disagreement exists between the calculations and the data from this experiment. {copyright} {ital 1997} {ital The American Physical Society}

We have measured the absolute cross section {sigma}({theta}) and complete sets of spin observables {ital A}{sub 00{ital i}{ital j}} in {sup 3}He({ital p},{ital p}) elastic scattering at energies of 200 and 500 MeV. The observables depend on linear combinations of six complex scattering amplitudes for the {ital p}-{sup 3}He system and provide a severe test of current reaction models. The in-scattering plane observables ({ital A}{sub 00{ital m}{ital m}}, {ital A}{sub 00{ital l}{ital l}}, {ital A}{sub 00{ital l}{ital m}}, and {ital A}{sub 00{ital m}{ital l}}) are all in quantitative disagreement with fully microscopic nonrelativistic optical model calculations and nonrelativistic distorted wave Born approximation calculations.

A polarized 3 He gas target of 6.44 atm pressure has been used to measure beam-and target-related asymmetries, A 00 N 0 and A 000 N , and spin correlation parameters, A 00 NN , for proton elastic scattering from 3 He. Between 200 and 500 MeV, and in the range of momentum transfers q = 2–5.1 fm −1 , differences between A 000 N and A 00 N 0 are found which provide unambiguous evidence for a significant f amplitude in p- 3 He scattering even though this amplitude vanishes for the NN system. The new target-related observables are only in fair agreement with results of two model calculations based on a non-relativistic momentum space optical potential and on a nonrelativistic distorted wave Born approximation model.

Coupled channel calculations for proton-nucleus inelastic scattering are performed using the Dirac formalism. The inelastic scattering of 362, 500, and 800 MeV protons from [sup 40]Ca, [sup 90]Zr, and [sup 208]Pb are considered. Transition potentials for the low-lying collective states are obtained using a simple collective model. Phenomenological as well as parameter-free relativistic impulse approximation (RIA) optical potentials are used for the direct potentials. It is found that reasonable descriptions of both elastic and inelastic observables are obtained. It is shown that the coupling to low-lying states greatly improves the agreement with the large angle data.

Historically, work in medium energy nucleon-nucleus scattering physics started in the 1950s and has continued since. During the past ten years exciting new developments have occurred, and this work reviews these developments. Two distinct theoretical approaches for describing the medium energy scattering process are discussed. The first is nonrelativistic and is based on approximate solutions to the many-body Schrodinger equation. The second is relativistic and is based on covariant meson exchange theory and the Dirac equation. A pedagogical discussion of nonrelativistic multiple scattering formalisms is presented, followed by a description of the approximation schemes used in numerical applications of the theory. Recent theoretical developments in the nonrelativistic approach, including medium corrections to the effective projectile-target nucleon interaction, off-shell contributions, and full integration (“full-folding”) of the nucleon-nucleus optical potential are discussed in detail. The historical development of the relativistic scattering models for the nucleon-nucleus system is reviewed and each of the principal models developed during the past ten years is explained, starting with the original relativistic impulse approximation model. We show direct comparisons, some previously unpublished, between the predictions of the best available nonrelativistic and relativistic scattering models and the data. A number of specific proton-nucleus elastic scattering cases are considered, including p+ 16 O, 40 Ca and 208 Pb at incident proton laboratory energies of 200, 500 and 800 MeV. Both relativistic and nonrelativistic approaches provide surprisingly similar and fairly good overall descriptions of the data. Finally, possible areas of further theoretical work in this field are discussed.

Analyzing powers (Ay) and spin-rotation-depolarization parameters (DSS, DSL, DLS, DLL, DNN) were determined for 500 MeV p + 2 H and p + 12 C inclusive quasielastic scattering at 10°, 15°, and 20° laboratory scattering angles. The p + 2 H data are consistent with the isospin-average of the proton-proton and proton-neutron scattering observables; the p + 12 C data are not. A relativistic plane wave impulse approximation calculation leads to better agreement with the p + 12 C spin-observables.

Various relativistic treatments are applied to deuteron-nucleus elastic scattering at intermediate energies. There are various possibilities for spin-one wave equations. Here we have considered three of them, the Kemmer-Duffin-Petiau, Proca, and Weinberg equations. Second-order equations are obtained from each using a similar set of approximations. Elastic-scattering observables including the differential cross section, and the vector and tensor analyzing powers are calculated using all three equations. The different predictions are compared with each other and with experimental data for 400 MeV $^{58}\mathrm{Ni}$(d,d${)}^{58}$Ni and 700 MeV $^{40}\mathrm{Ca}$(d,d${)}^{40}$Ca. We find that within the approximations made and for the assumed interactions there are no significant differences between the three sets of predicted observables.

Elastic and inelastic observables for the scattering of 500 MeV protons from $^{40}\mathrm{Ca}$ are calculated using either the first-order relativistic or nonrelativistic impulse approximation for the diagonal potentials and a collective model for the transition potentials. The calculations are done using either Dirac or Schr\"odinger coupled channel programs. The relativistic approach reproduces the inelastic observables better than the first-order nonrelativistic impulse approximation model.

We compute the analyzing power, ${\mathit{A}}_{\mathit{y}}$, and spin rotation, Q, for proton elastic scattering at 650 and 800 meV from target nuclei $^{16}\mathrm{O}$, $^{40}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$, using both nonrelativistic multiple-scattering theory and a relativistic impulse approximation model. We show that the nonrelativistic theory, based on the Schr\"odinger equation with relativistic kinematics, and the relativistic model, based on the Dirac equation, provide very similar and equally good descriptions of these spin observables when electromagnetic spin-orbit contributions are included in both approaches. The nonrelativistic model calculations include contributions from nuclear medium effects (Pauli blocking and binding energy corrections) and also target nucleon two-body correlations. Medium effects and correlations are not expected to be significant in the relativistic model based on the Dirac equation, and were not included.

A nonrelativistic nucleon-nucleon ({ital NN}) coupled channels isobar model is used to calculate nuclear medium corrections to the first-order Watson optical potential for nucleon-nucleus scattering. The {ital NN} interaction includes {pi}, 2{pi}, {rho}, {eta}, and {omega} exchange for the pure nucleonic sector, one-pion exchange for nucleon-isobar coupling, and phenomenological short-range interactions for both the diagonal and coupling terms. Good fits to {ital NN} elastic phase shifts from 0--1 GeV have been obtained with this model. The specific nuclear medium effects studied here include Pauli blocking of intermediate nucleon scattering states and off-shell binding energy shifts. On-momentum-shell matrix elements of the density dependent, effective {ital NN} {ital t} matrix are used to calculate the local proton-nucleus optical potential assuming the local density approximation. The model is applied to proton elastic scattering from {sup 16}O, {sup 40}Ca, {sup 48}Ca, and {sup 208}Pb at 320, 400, 500, 650, and 800 MeV and the predictions are compared with available data. In general, the medium modifications significantly affect the nonrelativistic predictions, even at 800 MeV, and bring about a substantial, overall improvement in the description of differential cross section and spin observable data. The improvements occur for each case and at all angles studied, butmore » the agreement is most successful for forward angle differential cross sections and for spin observable data from 1 to 3 fm{sup {minus}1}. Deficiencies remain in the density dependent, nonrelativistic predictions for the forward angle spin observables where relativistic models are quite successful. The relation of this work to other nonrelativistic models which include nuclear medium corrections, off-shell effects, and full-folding contributions is also discussed.« less

We report precision measurements of the polarization transfer parameter ${\mathit{D}}_{\mathit{NN}}$ for 500 MeV polarized proton elastic scattering from $^{12,13}\mathrm{C}$ at the first diffractive minima in the differential cross sections. The ratio ${\mathit{D}}_{\mathit{NN}}$${(}^{13}$C)/${\mathit{D}}_{\mathit{NN}}$${(}^{12}$C) (1.000\ifmmode\pm\else\textpm\fi{}0.028) is consistent with zero spin-flip probability (S) for $^{13}\mathrm{C}$, where S (1-${\mathit{D}}_{\mathit{NN}}$). Comparisons are made with results of theoretical calculations reported in the literature. \textcopyright{} 1996 The American Physical Society.

The elastic scattering observables for 400 MeV [pi][sup [plus minus]] on [sup 28]Si are calculated using a relativistic impulse approximation Kemmer-Duffin-Petiau formalism to calculate the [pi][sup [plus minus]] nucleus optical potential, and the Kemmer-Duffin-Petiau wave equation of motion with the aforementioned potential. The results are compared with recent experiments and with the results of nonrelativistic impulse approximation treatments.

The spin correlation parameter [ital A][sub 00[ital N][ital N]] for 497.5 MeV proton + proton elastic scattering was determined over the center-of-momentum scattering angle region 23.1[degree]--64.9 [degree]. The new [ital A][sub 00[ital N][ital N]] extend to more forward angles than existing [ital A][sub 00[ital N][ital N]] and have significantly smaller statistical errors ([plus minus]0.01--0.04). The [ital A][sub 00[ital N][ital N]] are qualitatively described by recent phase shift analyses, but a quantitative shape and normalization discrepancy remains in the forward angle region. These new data provide important constraints for nucleon-nucleon spin-dependent amplitudes at forward angles which are used in theoretical models of nucleon-nucleus scattering.

High quality analyzing power data ({Delta}{ital A}{sub {ital y}}{le}0.05) for 800 MeV {sup 208}Pb({ital {rvec p}},{ital p}{prime}) scattering to the 0{sup +} ground state and to the 3{sup {minus}} 2.61 MeV collective state were obtained for {theta}{sub c.m.}=22{degree} to 37{degree}, extending the range of momentum transfer out to 4.7 fm{sup {minus}1}. Theoretical predictions for these data were obtained using analyses based on both a nonrelativistic impulse approximation approach and a relativistic impulse approximation approach. For both the elastic and inelastic analyzing powers, the relativistic impulse approximation approach provided a better description at these large momentum transfers.

A progress report is given for the various components of the STAR detector system. We report on the recent developments in the detector proto-typing and construction, with an emphasis on the main TPC, recent TPC cosmic ray testing and shipping to Brookhaven National Laboratory

The 5-dimensional spin-0 form of the Kemmer-Duffin-Petiau (KDP) equation is used to calculate scattering observables [elastic differential cross sections ($d\sigma/d\Omega$), total cross sections ($\sigma_{Tot}$), and reaction cross sections ($\sigma_{Reac}$})] and to deduce $\sigma_{Tot}$ and $\sigma_{Reac}$ from transmission data for $K^+ + $ $^{6}$Li, $^{12}$C, $^{28}$Si, and $^{40}$Ca at several momenta in the range $488 - 714 MeV/c$. Realistic uncertainties are generated for the theoretical predictions. These errors, mainly due to uncertainties associated with the elementary $K^+ +$ nucleon amplitudes, are large, so that the disagreement that has been noted between experimental and theoretical $\sigma_{Tot}$ and $\sigma_{Reac}$ is not surprising. The results suggest that the $K^+ +$ nucleon amplitudes need to be much better determined before unconventional medium effects are invoked to explain the data., Comment: 7 pages text, 5 figures

An algorithm is presented to adjust the uncorrelated momentum vectors of identical bosons produced by models of relativistic heavy-ion collisions to reproduce two-body and three-body Bose-Einstein correlation functions. The method is used to study the quality of the three-body correlations predicted by calculations in which prescribed two-body correlation functions are fit and to study the effects on the two-body distributions when the three-body correlations help constrain the momentum vector adjustment procedure. {copyright} {ital 1996 The American Physical Society.}

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.

The study of nucleon-nucleus scattering at medium energies is one of the fundamental subjects in nuclear physics. As the incident nucleon energy becomes much greater than the Fermi energy of the nucleus, the interpretation of the scattering data in terms of the effective nucleon-nucleon (NN) interaction and nuclear structure should become more straightforward. Once the scattering process is well understood, analysis of the data might reveal new elements of nuclear structure and reaction dynamics.

Calculations are presented of the nuclear tensor term in the proton-nucleus optical model potential, generated by the relativistic impulse approximation. We first show that previously published expressions for this term make an unnecessary approximation, and second, clarify its effects in proton-nucleus elastic scattering at intermediate energies. The effects of the nuclear tensor term alone on the spin observables {ital A}{sub {ital y}} and {ital Q} for {ital p}+{sup 40}Ca and {sup 208}Pb targets, at 650- and 800-MeV incident laboratory energy are shown. We find that the overall effect of the nuclear tensor term is in general quite small, except for the heaviest target considered.

Angular distributions for the elastic and inelastic scattering of 0.8 GeV protons from /sup 24/Mg and /sup 26/Mg are presented. Cross sections for protons exciting states of energy up to about 10 MeV are measured using a high resolution spectrometer. Coupled channels analyses of scattering data to the 0/sup +/, 2/sup +/, 4/sup +/, and 6/sup +/ states in the ground state rotational band, the 2/sup +/, 3/sup +/, 4/sup +/, and 6/sup +/ states in the ..gamma..-vibrational band, the 0/sup +/, 2/sup +/, and 4/sup +/ states in the ..beta..-vibrational band, and the 3/sup -/ and 5/sup -/ members of the K/sup ..pi../ = 0/sup -/ and 3/sup -/ vibrational bands in /sup 24/Mg are presented. Also reported are coupled channels analyses of the experimental angular distributions in /sup 26/Mg for the 0/sup +/, 2/sup +/, and 4/sup +/ states in the ground state band, the possible 2/sup +/, 3/sup +/, and 4/sup +/, ..gamma..-band members, and several 3/sup -/ members of K/sup ..pi../ = 0/sup -/ and 3/sup -/ bands. The data for the 3/sup -/ states in both /sup 24/Mg and /sup 26/Mg differ both in shape and angular positions of the maxima and minima. Coupled channelsmore » analyses are able to account for these differences in the 3/sup -/ experimental cross sections by selecting K/sup ..pi../ = 0/sup -/ or 3/sup -/. This is believed to be the first observation of ''K dependence'' for l = 3 excitations in inelastic scattering by s-d shell nuclei. Distorted wave Born approximation analyses of the other states in /sup 26/Mg excited by l transfers from 2 to 4 are also described. Several new assignments of J/sup ..pi../ for excited states in /sup 26/Mg are proposed based upon the distinctive l transfer dependence found in the positions of the first maximum and in the general shapes of the angular distributions. Multipole moments extracted from the deformed optical potentials are related to those of the matter distributions by Satchler's theorem. These are compared to multipole moments obtained from analyses of hadronic scattering data, as well as with the moments of the charge distributions determined by electromagnetic measurements.« less

The elastic scattering of protons from 16 O, 40 Ca and 208 Pb at 800 MeV is analyzed using non relativistic, multiple scattering theory where virtual pair production-annihilation processes for the projectile are included as a relativistic correction. Second-order, target-nucleon correlation terms are also examined. The effects of these corrections on the predicted elastic scattering observables are evaluated.

In this application of Dirac phenomenology a relativistic impulse approximation is used to describe proton-nucleus elastic scattering at intermediate energies. The results demonstrate the superiority of this relativistic treatment over the nonrelativistic impulse approximation, especially with regard to spin observables. The method has important implications with respect to the extraction of neutron distributions.

Angular distribution data for 800 MeV $^{208}\mathrm{Pb}(p, {p}^{\ensuremath{'}})$ (2.61 MeV, ${3}^{\ensuremath{-}}$) are analyzed to determine the sensitivity of the analysis to the neutron component of the transition density. The analysis employs the first order Kerman, McManus, and Thaler optical potential model (distorted wave Born approximation together with the impulse approximation). The total error in the multipole moment of the deduced transition density, ${M}_{n}(E3)$, is computed based on uncertainties in (1) the elastic and inelastic scattering data, (2) the geometry of the transition density, (3) the nucleon-nucleon amplitudes, (4) the proton transition density, (5) correlation corrections, and (6) medium modifications to the effective interactions. Under the presumption of an accurate theoretical model, the minimal uncertainty in ${M}_{n}(E3)$ is \ifmmode\pm\else\textpm\fi{}8.5%. Such accuracy permits meaningful comparisons with results from nuclear structure theory.

The nonrelativistic multiple scattering formalism of Watson and Kerman, McManus, and Thaler is applied to the deuteron-nucleus elastic scattering system. An optical potential is constructed to second order in the nucleon-nucleon effective interaction t matrix and is organized in such a way that the usual Watanabe folding potential appears as the leading term. The Watanabe folding potential is constructed by integrating nucleon-nucleus optical potentials evaluated at half the deuteron incident kinetic energy over the deuteron s-state wave function. Corrections to the folding potential are identified which arise from deuteron-nucleon double scattering effects, the deuteron d state, virtual deuteron breakup, additional nuclear medium effects, additional target nucleon correlation effects, and relativistic processes. Many of these corrections do not appear in folding model approaches based on effective, rather than microscopic, deuteron-nucleus Hamiltonians. These additional multiple scattering corrections are second order in the nucleon-nucleon t matrix as is the case for the virtual deuteron breakup process which is often included in numerical calculations. Estimates of several of these additional multiple scattering corrections are provided for 700 MeV deuteron-nucleus elastic scattering. Most are found to be quite small. However, the additional effects of the nuclear medium beyond that already included in the input nucleon-nucleusmore » optical potentials are significant and are comparable in magnitude to the effects of virtual deuteron breakup. It is intended that this multiple scattering approach be applied to deuteron-nucleus elastic scattering at energies of several hundred MeV.« less

A previous study of the Coulomb interaction in nonrelativistic multiple-scattering theory is extended to account for relativistic effects. The projectile-nucleus Coulomb potential is computed from the relativistic M\o{}ller amplitude for projectile-nucleon scattering at low momentum transfer. The resulting Coulomb potential is reasonably approximated by folding $\frac{{e}^{2}}{|\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}}^{\ensuremath{'}}|}$ with the nuclear charge density, but must be multiplied by an additional kinematic factor to bring the corresponding projectile-nucleus Coulomb-scattering amplitude into agreement with relativistic results.

We present and discuss here the results of a calculation of the real part of the potential energy of a proton within nuclear matter, making use of the realistic Reid soft-core nucleon-nucleon interaction, which we justify in the intermediate-energy range. The problem of evaluating the volume of the real part of the proton-nucleus optical-model potential as a function of incident energy is solved with the help of a number of techniques previously developed in the literature of nuclear-matter theory. We find good agreement with results of various phenomenological studies over an energy range of 100 to 1050 MeV incident proton energy for targets $^{40}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$, which we adopt as test cases. Furthermore, we consider a number of higher-order corrections to our initial result; all of these have minimal effect in the energy regime we have considered except for the third-order correction proposed by Rajaraman, as we demonstrate and discuss. Finally, we show that the conventional approach to the nucleon-nucleus potential at medium energy, the so-called Rayleigh-Lax potential, which makes use of a straightforward impulse approximation and an empirical nucleon-nucleon scattering amplitude, is in gross disagreement both with phenomenological findings concerning the energy dependence of the optical potential and with results of the present calculations. We make an effort to shed some light on the physical reasons for the failure of the Rayleigh-Lax approach, as opposed to the success of other approaches relying upon realistic nucleon-nucleon interactions or phase shifts rather than an empirical medium-energy nucleon-nucleon $T$ matrix.[NUCLEAR REACTIONS $^{40}\mathrm{Ca}(p,p)$, $^{208}\mathrm{Pb}(p,p)$, $E=100\ensuremath{-}1050$ MeV; nuclear matter approach used to estimate volume of real part proton-nucleus optical model potential, multiple-scattering formalism, numerical estimates of various higher-order terms.]

Results of relativistic and nonrelativistic impulse approximation calculations are compared for p+/sup 40/Ca elastic scattering observables between 181 and 1040 MeV. At 400 MeV and above the relativistic approach is superior, especially with regard to spin observables. Below 400 MeV neither calculation agrees well with experiment.

Large angle elastic differential cross section and analyzing power data are reported for 497.5 MeV p-arrow-right+/sup 40/Ca. The characteristic diffraction pattern extends to the largest momentum transfer, 5.3 fm/sup -1/. Theoretical models which incorporate either relativistic or nonrelativistic dynamics do not quantitatively describe the data for q>3.5 fm/sup -1/. Possible explanations for the discrepancy are suggested

The 500 MeV effective nucleon-nucleon isoscalar interaction is investigated through nonrelativistic folding model analyses of p+nucleus elastic scattering data. Three empirical interactions are deduced. The first, obtained from a relativistic-Schroedinger-equation-equivalent form of a phenomenological Dirac optical potential, contains terms which are dependent on the square of the nuclear matter density. A modified version of this interaction is then obtained, in which the density dependence is made explicit. Finally, an optical potential is deduced which depends linearly on the density, resulting in a density-independent nucleon-nucleon effective interaction. Nuclear size information inferred from calculations using these effective interactions is found to be in reasonable agreement with theoretical expectations. The relative merits of each of these three forms of the interaction are discussed.

Different descriptions of the reaction /sup 28/Si(/sup 13/C, /sup 12/C)/sup 29/Si at 36 MeV leading to the ground and first excited states of /sup 29/Si are examined. Sensitivity of the reaction cross section to various families of optical parameters is investigated and the so-called ''surface transparent potential'' is used as an alternate treatment. Exact finite range distorted-wave Born approximation and coupled-channels Born approximation analyses of the reaction are performed, showing that the coupled-channels Born approximation analysis, even in its presently restricted form, leads to an improvement over the distorted-wave Born approximation predictions. (AIP)

Angular distributions for the elastic and inelastic scattering of 800 MeV protons from /sup 24/Mg are presented. Results of distorted-wave Born-approximation (DWBA) and coupled-channels (CC) analyses of the data for the 0/sup +//sub 1/, 2/sup +//sub 1/, 4/sup +//sub 1/, and 6/sup +//sub 1/ members of the ground state rotational band, the 2/sup +//sub 2/, 3/sup +//sub 2/, 4/sup +//sub 2/, and 5/sup +//sub 2/ members of the ..gamma.. band and the 0/sup +/ member of the ..beta.. band are discussed, and the effects of ground state deformation and multistep contributions are assessed. The DWBA calculations for the 4/sup +//sub 1/ and 6/sup +//sub 1/ angular distributions fail to even qualitatively reproduce the data, while a CC calculation, using a symmetric rotator model with quadrupole and hexadecapole ground state deformations, provides good fits for the 0/sup +//sub 1/, 2/sup +//sub 1/, and 4/sup +//sub 1/ angular distributions. A CC calculation in which the ground band is coupled to the ..gamma.. band, with an assumed asymmetric vibrational amplitude, gives a fair fit to the data for the 2/sup +//sub 2/ state, but fails to fit the 3/sup +//sub 2/, 4/sup +//sub 2/, and 5/sup +//sub 2/ data. This failure in themore » calculation may be due to the lack of a direct step to the 4/sup +//sub 2/ state, as well as neglect of the spin-flip process. The result of coupling the ground band with the 6.43 MeV 0/sup +//sub ..beta../ state indicates that this axially symmetric deformed vibrational model may be essentially correct, but also seems to indicate that a direct 0/sup +//sub 1/-0/sup +//sub ..beta../ step needs to be considered, based on the behavior of the forward angle 0/sup +//sub ..beta../ data. Additional coupling of a 2/sup +//sub ..beta../ state does not dramatically improve the fit to the 0/sup +//sub ..beta../ data. The results obtained here from analyses of the 800 MeV data are compared with those obtained through analyses of lower energy data.« less

The second order Kerman, McManus and Thaler optical potential model is used in the analysis of 800 MeV proton elastic scattering data from 144,154 Sm. Correlation terms arising from the large intrinsic deformation of 154 Sm are included and are found to be quite significant. Neutron isotopic density distribution and rms radius differences are determined and are seen to be in good agreement with deformed basis, Hartree-Fock predictions.

Medium energy proton elastic and inelastic scattering to states of 58 Ni and 208 Pb, and 4 He elastic and inelastic scattering to states of 40 Ca, are analyzed using the partial wave approach, by solving the Schrodinger equation with relativistic kinematics and using the distorted wave Born approximation. Our results can be compared with results of several previous analyses of the nucleon inelastic data using the Glauber approximation. Our calculations are absolute, using nuclear collective parameters obtained from a survey of a large number of low-energy analyses of inelastic scattering of electrons, nucleons and nuclei from 40 Ca, 58 Ni and 208 Pb.

Lorentz vector and scalar, isovector and isoscalar proton-nucleus optical potentials are obtained from invariant nucleon-nucleon amplitudes using a relativistic impulse approximation. Cross sections, analyzing powers, and spin rotation functions for $^{90}\mathrm{Zr}$(p,p) and the $^{90}\mathrm{Zr}$(p,n)$^{90}\mathrm{Nb}$ (isobaric analog state) reaction at 160 and 500 MeV are calculated using a relativistic generalization of the Lane equations. These predictions are compared to nonrelativistic impulse approximation results and to experimental data at 160 MeV.