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Analyzing powers and cross sections for the elastic scattering of polarized 7 Li by targets of 6 Li, 7 Li and 12 C are shown to depend only on the properties of the projectile for momentum transfers of less than 1.0 fm −1 . The result of a detailed analysis of the experimental data within the framework of the coupled channels model with ground state reorientation and transitions to the excited states of the projectile and targets included in the coupling schemes are presented. This work suggests that nuclear properties of weakly-bound nuclei can be tested by elastic scattering experiments, independent of the target used, if data are acquired for momentum transfers less than ∼ 1.0 fm −1 .

Primary standards for 7Li polarimetry requiring a measurement of the reaction p(7Lio,a)at03 to the beamline imposeexcessiveradiationdamageonthedetectors.Eliminatingthisdamagerequirestheestablishmentofsecondarystandardsfortheonlinemeasurementofbeampolarization.Acompletesetofanalyzingpowershasbeenobtainedforthescatteringofpolarized7Liby4Hetothe4.63MeVexcitedstateof7Liatabombardingenergyof31.5MeV.Certainanglesatwhichboth the di!erential cross-sections and analyzing powers are large are tabulated as secondary polarization stan-dards. ( 2001 Elsevier Science B.V. All rights reserved. Keywords: Polarized 7Li polarimetry 1. IntroductionEstablishing the magnitude and sign of a beam’spolarizationis now largelyroutinedue tothe greate!ort that has gone into establishing primary po-larization standards for beams of spin 12,1or32nuclei. For heavy-ion beams of spin 32nuclei, thepioneering experimental work of the Heidel-berg}Marburg group showed that angular mo-mentum conservation rules allow a beam tensorpolarization to be determined from measurementsat03or1803[1}3].Theirexperimentswithpolariz-ed7Liand23Nabeamsshowedmanynovelphysicse!ects. Perhaps one of the most startling was thatvirtual projectile excitations can lead to large ana-lyzing powers even when the spin}orbit force issmall [4,5]. Recent experimental work on under-standing the structure of loosely boundhalo nuclei[6] has rekindled interest in studies involving thestable but loosely bound nuclei 6,7Li.All 7Li beam standards are currently based onthe fact that for the p(7Lio,a)a reaction induced bya tensor polarized beam, the tensor analyzingpowers are „20"!1 and

A complete set of analyzing powers (AP`s), {ital iT}{sub 11}, {ital T}{sub 20}, {ital T}{sub 21}, and {ital T}{sub 22}, for 50 MeV {sup 12}C({sup 6}Li(vector),{sup 6}Li) elastic scattering and inelastic scattering to the {sup 12}C(2{sup +}, 4.44 MeV), {sup 12}C(0{sup +}, 7.65 MeV), and {sup 12}C(3{sup {minus}}, 9.64 MeV) states over the center-of-mass (c.m.) angular range 10{degree}{endash}115{degree} is reported. In addition, cross sections for the excited states 3{sup +}(2.18 MeV), 2{sup +}(4.31 MeV), and 1{sup +}(5.65 MeV) of {sup 6}Li were measured by using the inverse-kinematics reaction {sup 6}Li({sup 12}C,{sup 12}C) at 100 MeV. A combined analysis of the new 50 MeV data and previous 30 MeV data has been carried out using the coupled-channels (CC) code FRESCO. The CC calculations use an optical potential with double-folded (DF) real central, Woods-Saxon imaginary central, and Thomas real spin-orbit (SO) potentials. Calculations include reorientation terms and coupling to the first three excited states of {sup 6}Li and the first two nonzerospin states of {sup 12}C. The {sup 6}Li coupling strengths were fixed by the measured {sup 6}Li excited-state cross sections. The elastic-scattering cross sections and A.P.`s are described well. The need for an explicit SO potential is apparent in the elasticmore » and inelastic-scattering AP`s {ital iT}{sub 11}, more so at 30 MeV than at 50 MeV. The rank-2 AP`s up to 50{degree} c.m. arise mainly from ground-state reorientation effects. The DF potential normalization constant {ital N} approaches unity for the 50 MeV data. At both energies, the {sup 12}C(2{sup +}) cross sections are underestimated at large angles, and the description of the {sup 12}C(3{sup {minus}}) cross sections is poor in detail. The {sup 12}C(3{sup {minus}}) AP`s and the {sup 12}C(2{sup +}) {ital iT}{sub 11} are not reproduced at either energy. {copyright} {ital 1996 The American Physical Society.}« less

A complete set of analyzing powers (i${\mathrm{T}}_{11}$, ${\mathrm{T}}_{20}$, ${\mathrm{T}}_{21}$, and ${\mathrm{T}}_{22}$) are reported for the elastic scattering of 50 MeV $^{6}\ensuremath{\rightarrow}$ by $^{12}\mathrm{C}$. They are as large as or larger than those measured earlier for 30 MeV $^{6}\ensuremath{\rightarrow}$. A combined optical model analysis of both energies shows ${\mathrm{T}}_{21}$ to arise from the tensor interaction, ${\mathrm{T}}_{20}$ to involve a combination of tensor and J-dependent interactions, and i${\mathrm{T}}_{11}$ to be the most complicated, arising from an explicit spin-orbit, as well as tensor and J-dependent interactions. A coordinate transformation of the data and calculations, suggested in the earlier work of Hooton and Johnson, provides the clearest evidence for the need of a tensor interaction to describe $^{6}\ensuremath{\rightarrow}$ scattering. Examining the optical model calculations in terms of transferred angular momentum amplitudes provides further insight into the role played by each interaction. Also presented are the analyzing powers for the $^{4}\mathrm{He}$${(}^{6}$Li${,}^{4}$He) polarimeter reaction at this higher bombarding energy.

Vector and tensor analyzing powers ([ital iT][sub 11], [ital T][sub 20], [ital T][sub 21], and [ital T][sub 22]) for [sup 6]L[rvec i]+[sup 12][ital C] elastic scattering are presented for a [sup 6]L[rvec i] bombarding energy of 30 MeV over the c.m. angular range 15[degree]--138[degree]. The results of optical model calculations made with central, spin-orbit, tensor and angular momentum dependent potential terms show that the large angle data for the vector and tensor analyzing powers are sensitive to the presence of a static spin-orbit term. The nonzero [ital T][sub 21] data show that a tensor potential must be included to describe [sup 6]Li scattering.

Reactions with the spin structure 1 + + 0 + → 0 + + 0 + have properties which allow an absolute determination of ∣ iT 11 ∣ via measurement of two of the tensor analyzing powers. Vector analyzing powers of the 12 C ( 6 L i , α 3 ) 14 N reaction are deduced to accuracies of about 6% from measurements of the tensor analyzing powers T 20 and T 21 at E Li = 33 MeV. The vector analyzing power in 6 L i + 4 He elastic scattering is measured at E c.m. = 6.2 MeV and θ c.m. = 150°, establishing a secondary standard convenient for fast monitoring of 6 Li vector polarization.

Mechanisms for the loss of polarization of beams of nuclear spin polarized 6,7 Li accelerated by the FSU tandem Van de Graaff superconducting linac heavy-ion accelerator are considered. The linac uses superconducting solenoids for radial focusing. Estimates and detailed calculations show that for most experiments the depolarization due to the conventional beam line is negligible, while, provided account is taken of the precession produced by the solenoids, the depolarization due to the linac is negligible for 6 Li 3+ and small for 7 Li 3+ . An experiment was carried out to investigate the depolarization of a vector polarized 6 Li 3+ beam due to acceleration by the linac. No loss of polarization was observed.

The dye-laser optically pumped polarized 6,7 Li − ion source of the FSU tandem-linac heavy-ion accelerator has completed its first year of operation. The ion source has produced highly polarized beams of 6 Li for nuclear physics experiments with on-target currents of 6 Li 3+ greater than 150 nA. Absolute measurements of the on-target 6 Li polarization have yielded P yy = −1.33± 0.02 and P y > 0.74 ± 0.03 for the nuclear tensor and vector polarization, respectively. No loss of polarization due to acceleration by the linac booster was observed.

Vector and tensor analyzing powers ([ital iT][sub 11], [sup [ital T]T][sub 20], [ital T][sub 20], and [ital T][sub 22]) for the [sup 9]Be([sup 6]L[rvec i],[sup 6]He)[sup 9]B reaction are presented for a [sup 6]L[rvec i] bombarding energy of 32 MeV over the angular range from 14[degree] to 80[degree] c.m. A one-step reaction calculation is consistent with the angular distribution and vector analyzing power [ital iT][sub 11] for the ground-state transition but does not describe the tensor analyzing power [sup [ital T]T][sub 20]. Coupled channels calculations that include inelastic coupling in the entrance and exit channels do not reproduce either the vector or tensor analyzing powers. Sequential transfer calculations via ([sup 6]Li,[sup 7]Li)([sup 7]Li,[sup 6]He) do not reproduce the ground-state angular distribution but do reproduce the analyzing powers. The analyzing power data to the [sup 9]B(5/2[sup [minus]], 2.36 MeV state) are well reproduced by the coupled channels calculation although the cross section is under predicted by a factor of 3.

An optically-pumped polarized lithium ion source has been built and is currently producing highly polarized 6 Li − beams with on-target 6 Li 3+ currents up to 150 nA. An absolute measurement of the on-target tensor polarization was made during a one week calibration run, which yielded t 20 = −0.938±0.013, averaged over the entire run. The on-target vector polarization is typically t 10 = 1.02±0.06. The nuclear polarization of the atomic beam at the source has been measured by laser-induced fluorescence to be typically t 10 = 1.14±0.06 and t 20 = −1.14±0.06. A 4 He gas polarimeter has been calibrated as a secondary standard for monitoring both vector and tensor polarizations.

A laser-optically-pumped polarized lithium ion source is being developed to provide beams of nuclear polarized 6,7Li− for injection into the FSU tandem Van de Graaff-linac. Electro-optically modulated, circularly polarized light optically pumps a lithium atomic beam into a single magnetic substate, M I = I, M J = 1 2 . No inhomogeneous magnetic field (sextupole or quadrupole Adiabatic rf transitions enable the polarization to be changed by transferring the population into different magnetic substates. Using a second electro-optic to modulate a second beam from the same laser, and Zeeman tuning, the polarization of the atomic beam is obtained by laser induced fluorescence. The polarized atomic beam is ionized to Li+ and then charge exchanged to Li−.

A radio-frequency ion source using electrostatic inflection has been operated in the terminal of a model FN tandem Van de Graaff accelerator. This arrangement is useful for high resolution resonance experiments in atomic and low energy nuclear physics and for hydrogen profiling using the the 6.4 MeV 1 H( 15 N, αγ) 12 C reaction.

Complete sets of analyzing powers have been obtained for a large number of inelastic scattering and single-nucleon stripping channels for 34-MeV polarized ${}^{7}\mathrm{Li}{+}^{12}\mathrm{C}.$ We present data for inelastic excitation to the 0.478-MeV ${1/2}^{\ensuremath{-}}$ state of ${}^{7}\mathrm{Li},$ the 4.44-MeV ${2}^{+},$ 7.65-MeV ${0}^{+},$ and 9.64-MeV ${3}^{\ensuremath{-}}$ states of ${}^{12}\mathrm{C}$ and for mutual excitation of the ${1/2}^{\ensuremath{-}}$ and ${2}^{+}$ states, single-neutron stripping to the 0.0-MeV ${1/2}^{\ensuremath{-}},$ 3.09-MeV ${1/2}^{+},$ and 3.85-MeV ${5/2}^{+}$ states and an unresolved multiplet centered at 7.6 MeV of ${}^{13}\mathrm{C},$ and single-proton stripping to the 0.0-MeV ${1/2}^{\ensuremath{-}}$ state and an unresolved doublet of the 3.51-MeV ${3/2}^{\ensuremath{-}}$ and 3.55-MeV ${5/2}^{+}$ states of ${}^{13}\mathrm{N}.$ These data are analyzed with the continuum-discretized-coupled-channels approach using cluster-folding model form factors in a calculation that includes all the known physics for these systems.

The elastic scattering vector analyzing powers for /sup 6/Li+/sup 16/O at 25.7 MeV and /sup 6/Li+/sup 12/C at 30 MeV have been measured. In addition, measurement of the vector analyzing power for inelastic /sup 6/Li scattering has been made for the 2/sup +/ (4.44 MeV) state in /sup 12/C. Excitation function data for /sup 6/Li+/sup 16/O elastic and inelastic scattering have also been measured at five angles for /sup 6/Li lab energies through the range 15--28 MeV in 375 keV steps. These data show the system to be resonance free at 25.7 MeV. The data have been analyzed in the coupled channels framework, employing the double folding model for the real part of the nuclear scattering potential. The coupling strengths in the coupled channels calculations were determined from inelastic scattering cross-section data directly. The elastic scattering vector analyzing powers arise from a complicated interference between channel coupling and spin-orbit contributions, whereas the /sup 12/C, 2/sup +/ inelastic vector analyzing power arises from the spin-orbit potential only. Inelastic scattering analyzing powers may allow the shape and strength of heavy-ion spin-orbit potentials to be investigated more clearly than do the elastic scattering analyzing powers. The normalization of the double-folded real potential wasmore » found to be in the range 0.85--1.00 in the coupled channel calculations, thus bringing the normalization of /sup 6/Li scattering into agreement with other projectiles.« less

The dependence of the vector polarization produced in the weak field transition region on the direction of the static field gradient is investigated by means of experimental measurements and numerical calculations for a lithium source. The measurements employ a weak field transition apparatus whose tapered magnet is outside the vacuum and hence easily reversed and calculations are performed for several existing polarized ion sources. The results demonstrate that while the vector polarization depends on the direction of the static field gradient under nonadiabatic conditions, this dependence vanishes in the adiabatic limit. It is shown that the positive field gradient consistently produces higher vector polarization and that the independence of the vector polarization on the direction of the field gradient under adiabatic conditions provides a sensitive experimental test of the adiabatic operation of a vector polarized ion source.

A ground state atomic beam source for producing polarized 6 Li nuclei is described. Representative data which cross calibrates three existing sources for 6 Li → + 12 C at 20 MeV are presented. Possible future systems for producing polarized heavy-ion beams are discussed.

Recently a certain class of homogeneous world models filled with perfect fluid have been discussed, [1, 2]. The corresponding results when anisotropic stresses are included are now examined.