arXiv subjects

J. L. Friar

Publications and source records attributed to J. L. Friar.

At least 55 records · Page 3Linked to original sources

arXiv1998

Nuclear Scales

Nuclear scales are discussed from the nuclear physics viewpoint. The conventional nuclear potential is characterized as a black box that interpolates nucleon-nucleon (NN) data, while being constrained by the best possible theoretical input. The latter consists of the longer-range parts of the NN force (e.g., OPEP, TPEP, the $π$-$γ$ force), which can be calculated using chiral perturbation theory and gauged using modern phase-shift analyses. The shorter-range parts of the force are effectively parameterized by moments of the interaction that are independent of the details of the force model, in analogy to chiral perturbation theory. Results of GFMC calculations in light nuclei are interpreted in terms of fundamental scales, which are in good agreement with expectations from chiral effective field theories. Problems with spin-orbit-type observables are noted.

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arXiv1998

The $A_y$ Puzzle and the Nuclear Force

The nucleon-deuteron analyzing power $A_y$ in elastic nucleon-deuteron scattering poses a longstanding puzzle. At energies $E_{lab}$ below approximately 30 MeV $A_y$ cannot be described by any realistic NN force. The inclusion of existing three-nucleon forces does not improve the situation. Because of recent questions about the $^3P_J$ NN phases, we examine whether reasonable changes in the NN force can resolve the puzzle. In order to do this we investigate the effect on the $^3P_J$ waves produced by changes in different parts of the potential (viz., the central force, tensor force, etc.), as well as on the 2-body observables and on $A_y$. We find that it is not possible with reasonable changes in the NN potential to increase the 3-body $A_y$ and at the same time to keep the 2-body observables unchanged. We therefore conclude that the $A_y$ puzzle is likely to be solved by new three-nucleon forces, such as those of spin-orbit type, which have not yet been taken into account.

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arXiv1997

Electromagnetic Corrections to the One-Pion-Exchange Potential

Leading-order electromagnetic loop corrections to the one-pion-exchange potential are computed within the framework of chiral perturbation theory. These corrections generate an effective nucleon-nucleon potential, $V_{πγ}$, which supplements the sum of OPEP and the nucleon-nucleon Coulomb potential. This potential is charge dependent and its construction is demonstrated to be gauge invariant. The potential $V_{πγ}$ has been included in the Nijmegen partial-wave analysis of np data. A particular renormalization scheme is chosen that leads to a negligible change in the charged-piNN coupling constant and in the np 1S0 scattering length and effective range.

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arXiv1997

Higher-Order Nuclear-Size Corrections in Atomic Hydrogen

Nuclear-size corrections of order $(Z α)^5$ and $(Z α)^6$ to the S-state levels of hydrogenic atoms are considered. These nuclear-elastic contributions are somewhat smaller than the polarizability (nuclear-inelastic) corrections for deuterium, but are of comparable or larger size for the hydrogen case. For deuterium the (attractive) nonrelativistic $(Z α)^5$ correction to the 2S-1S transition is 0.49 kHz, while the (repulsive) relativistic $(Z α)^6$ contribution is -3.40 kHz. For the proton the corresponding corrections are 0.03 kHz and -0.61 kHz, respectively. The $(Z α)^5$ contribution largely cancels the Coulomb-retardation part of the nuclear-polarization correction.

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arXiv1997

Nuclear Sizes and the Isotope Shift

Darwin-Foldy nuclear-size corrections in electronic atoms and nuclear radii are discussed from the nuclear-physics perspective. Interpretation of precise isotope-shift measurements is formalism dependent, and care must be exercised in interpreting these results and those obtained from relativistic electron scattering from nuclei. We strongly advocate that the entire nuclear-charge operator be used in calculating nuclear-size corrections in atoms, rather than relegating portions of it to the non-radiative recoil corrections. A preliminary examination of the intrinsic deuteron radius obtained from isotope-shift measurements suggests the presence of small meson-exchange currents (exotic binding contributions of relativistic order) in the nuclear charge operator, which contribute approximately 1/2%.

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arXiv1997

Nuclear Polarizabilities and Logarithmic Sum Rules

The electric polarizability and logarithmic mean-excitation energy are calculated for the deuteron using techniques introduced in atomic physics. These results are then used to improve limits on the atomic-deuterium frequency shift due to nuclear polarization in the unretarded dipole limit, as well as confirming previous results.

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arXiv1997

Higher-Order Nuclear-Polarizability Corrections in Atomic Hydrogen

Nuclear-polarizability corrections that go beyond unretarded-dipole approximation are calculated analytically for hydrogenic (atomic) S-states. These retardation corrections are evaluated numerically for deuterium and contribute -0.68 kHz, for a total polarization correction of 18.58(7) kHz. Our results are in agreement with one previous numerical calculation, and the retardation corrections completely account for the difference between two previous calculations. The uncertainty in the deuterium polarizability correction is substantially reduced. At the level of 0.01 kHz for deuterium, only three primary nuclear observables contribute: the electric polarizability, $α_E$, the paramagnetic susceptibility, $β_M$, and the third Zemach moment, $< r^3 >_{(2)}$. Cartesian multipole decomposition of the virtual Compton amplitude and its concomitant gauge sum rules are used in the analysis.

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arXiv1997

Reply to Baur's and Bertulani's Comment

Shortcomings of a momentum-space treatment of strong absorption, as discussed in the previous Comment [nucl-th/9611025], are only of concern at low projectile energies, $γ$< 1.5. At intermediate and high energies, for which the quantum-mechanical equivalent-photon spectrum is intended, the quantum-mechanical cross sections are reduced relative to the semi-classical results whether one treats strong effects via a momentum-space or an impact-parameter (spatial) cut-off. At these energies the origin of the discrepancy between the predictions of full quantuym-mechanical and the semi-classical calulations cannot be traced to differences in the treatment of strong-interaction effects. Rather, they arise from quantum effects neglected in the semi-classical calculations.

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arXiv1996

The $p p \to p pπ^0$ Reaction near Threshold: A Chiral Power Counting Approach

We use power-counting arguments as an organizing principle to apply chiral perturbation theory, including an explicit $Δ$, to the $p p \rightarrow p p π^0$ reaction near threshold. There are two lowest-order leading mechanisms expected to contribute to the amplitude with similar magnitudes: an impulse term, and a $Δ$-excitation mechanism. We examine formally sub-leading but potentially large mechanisms, including pion-rescattering and short-ranged contributions. We show that the pion-rescattering contribution is enhanced by off-shell effects and has a sign opposite to that of a recent estimate based on a PCAC pion interpolating field. Our result is that the impulse term interferes destructively with the pion rescattering and $Δ$-excitation terms. In addition, we have modeled the short-ranged interaction using $σ$ and $ω$ exchange mechanisms. A recoil correction to the impulse approximation is small. The total amplitude obtained including all of these processes is found to yield cross sections substantially smaller than the measured ones.

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arXiv1996

Dimensional Power Counting in Nuclei

Weinberg's dimensional power counting for nuclei is reprised in this primer. The role of QCD and chiral symmetry in constructing effective Lagrangians is discussed. The two-scale hypothesis of Manohar and Georgi is combined with power counting in amplitudes to shed light on the scales of nuclear kinetic and potential energies, the size of strong-interaction coupling constants, the size of meson-exchange currents, and the relative sizes of $N$-nucleon forces. Numerous examples are worked out and compared to conventional nuclear models.

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arXiv1996

A Quantum-Mechanical Equivalent-Photon Spectrum for Heavy-Ion Physics

In a previous paper, we calculated the fully quantum-mechanical cross section for electromagnetic excitation during peripheral heavy-ion collisions. Here, we examine the sensitivity of that cross section to the detailed structure of the projectile and target nuclei. At the transition energies relevant to nuclear physics, we find the cross section to be weakly dependent on the projectile charge radius, and to be sensitive to only the leading momentum-transfer dependence of the target transition form factors. We exploit these facts to derive a quantum-mechanical ``equivalent-photon spectrum'' valid in the long-wavelength limit. This improved spectrum includes the effects of projectile size, the finite longitudinal momentum transfer required by kinematics, and the response of the target nucleus to the off-shell photon.

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arXiv1996

Assessment of Triton Potential Energy

An assessment is made of the dominant features contributing to the triton potential energy, with the objective of understanding qualitatively their origins and sensitivities. Relativistic effects, short-range repulsion, and OPEP dominance are discussed. A determination of the importance of various regions of nucleon-nucleon separation is made numerically.

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arXiv1996

Nuclear Forces and Chiral Theories

Recent successes in {\it ab initio} calculations of light nuclei (A=2-6) will be reviewed and correlated with the dynamical consequences of chiral symmetry. The tractability of nuclear physics evinced by these results is evidence for that symmetry. The relative importance of three-nucleon forces, four-nucleon forces, multi-pion exchanges, and relativistic corrections will be discussed in the context of effective field theories and dimensional power counting. Isospin violation in the nuclear force will also be discussed in this context.

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arXiv1996

Dimensional Regularization and Nuclear Potentials

It is shown how nucleon-nucleon potentials can be defined in N dimensions, using dimensional regularization to continue amplitudes. This provides an easy way to separate out contact ($δ$-function) terms arising from renormalization. An example is worked out several ways for the case of two scalar particles exchanged between nucleons, which involves a very simple loop calculation. This leads to a Feynman-parameterized representation for the nucleon-nucleon potential. Alternately, a dispersion representation can be developed leading to a different, though equivalent, form.

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arXiv1996

Phenomenological Aspects of Isospin Violation in the Nuclear Force

Phenomenological Lagrangians and dimensional power counting are used to assess isospin violation in the nucleon-nucleon force. The $πNN$ coupling constants (including the Goldberger-Treiman discrepancy), charge-symmetry breaking, and meson-mixing models are examined. A one-loop analysis of the isospin-violating $πNN$ coupling constants is performed using chiral perturbation theory. Meson-mixing models and the $^3$He - $^3$H mass difference are also discussed in the context of naturalness.

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arXiv1995

QCD Scales in Finite Nuclei

The role of QCD scales and chiral symmetry in finite nuclei is examined. The Dirac-Hartree mean-field coupling constants of Nikolaus, Hoch, and Madland (NHM) are scaled in accordance with the QCD-based prescription of Manohar and Georgi. Whereas the nine empirically-based coupling constants of NHM span thirteen orders of magnitude, the scaled coupling constants are almost all {\it natural}, being dimensionless numbers of order one. We speculate that this result provides good evidence that QCD and chiral symmetry apply to finite nuclei.

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arXiv1994

Pedagogical Studies of Relativistic Hamiltonians

Relativistic Hamiltonians are defined as the sum of relativistic one-body kinetic energies, two- and many-body interactions and their boost corrections. We review the calculation of the boost correction of the two-body interaction from commutation relations of the Poincare group and show that its important terms can be easily understood from classical relativistic mechanics. The boost corrections for scalar- and vector- meson-exchange interactions, obtained from relativistic field theory, are shown to be in agreement with the results of the classical calculation. These boost corrections are also shown to be necessary to reproduce the known results of relativistic mean-field theories. We conclude with comments on the relativistic boost operator for the wave function of a nucleus. Several of the results presented in this pedagogical article are known. We hope that a better understanding of relativistic Hamiltonians and their relation to relativistic field theory is obtained by putting them together with a few new relations.

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arXiv1994

Few-Body Physics -- Then and Now

A summary of the XIV\underline{th} International Conference on Few-body Problems In Physics is given, with an emphasis on the important problems solved recently and the prognosis for the future of the field. Personal remarks and ``homework'' problem assignments are made.

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