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J. Golak

Publications and source records attributed to J. Golak.

At least 91 records · Page 5Linked to original sources

Treatment of the proton-proton Coulomb force in proton-deuteron breakup Faddeev calculations

We extend our approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) Faddeev calculations from elastic proton-deuteron (pd) scattering to the breakup process. The main new ingredient is a 3-dimensional screened pp Coulomb t-matrix obtained by a numerical solution of the 3-dimensional Lippmann-Schwinger equation. We demonstrate numerically that the proton-deuteron breakup observables can be determined from the resulting on-shell 3N amplitudes increasing the screening radius. However, contrary to the pd elastic scattering, the screening limit exists only after renormalisation of the pp t-matrices.

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A novel treatment of the proton-proton Coulomb force in elastic proton-deuteron Faddeev calculations

We propose a novel approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) Faddeev calculations. The main new ingredient is a 3-dimensional screened pp Coulomb t-matrix obtained by a numerical solution of the 3-dimensional Lippmann-Schwinger (LS) equation. We demonstrate numerically and provide analytical insight that the elastic proton-deuteron (pd) observables can be determined directly from the resulting on shell 3N amplitude increasing the screening radius. The screening limit exists without the need of renormalisation not only for observables but for the elastic pd amplitude itself.

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A New Treatment of 2N and 3N Bound States in Three Dimensions

The direct treatment of the Faddeev equation for the three-boson system in 3 dimensions is generalized to nucleons. The one Faddeev equation for identical bosons is replaced by a strictly finite set of coupled equations for scalar functions which depend only on 3 variables. The spin-momentum dependence occurring as scalar products in 2N and 3N forces accompanied by scalar functions is supplemented by a corresponding expansion of the Faddeev amplitudes. After removing the spin degrees of freedom by suitable operations only scalar expressions depending on momenta remain. The corresponding steps are performed for the deuteron leading to two coupled equations.

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The exact three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential in the screening limit

The three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived together with its asymptotic form without reference to partial wave expansion. The numerical solutions of the three-dimensional Lippmann-Schwinger equation for increasing cut-off radii provide half-shell t-matrices which are in quite a good agreement with the asymptotic values.

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Investigation of the Exclusive ^{3}He(e,e'pn)p Reaction

Cross sections for the ^{3}He(e,e'pn)p reaction were measured for the first time at energy transfers of 220 and 270 MeV for several momentum transfers ranging from 300 to 450 MeV/c. Cross sections are presented as a function of the momentum of the recoil proton and the momentum transfer. Continuum Faddeev calculations using the Argonne V18 and Bonn-B nucleon-nucleon potentials overestimate the measured cross sections by a factor 5 at low recoil proton momentum with the discrepancy becoming much smaller at higher recoil momentum.

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Proton-proton scattering without Coulomb force renormalization

We demonstrate numerically that proton-proton (pp) scattering observables can be determined directly by standard short range methods using a screened pp Coulomb force without renormalization. In examples the appropriate screening radii are given. We also numerically investigate solutions of the 3-dimensional Lippmann-Schwinger (LS) equation for a screened Coulomb potential alone in the limit of large screening radii and confirm analytically predicted properties for off-shell, half-shell and on-shell Coulomb t-matrices. These 3-dimensional solutions will form a basis for a novel approach to include the pp Coulomb interaction into the 3N Faddeev framework.

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Lorentz Boosted Nucleon-Nucleon T-matrix and the Triton Binding Energy

The phase equivalent relativistic NN potential, which is related by a nonlinear equation to the original nonrelativistic potential, is used to construct the mass operator (rest Hamiltonian) of the 3-nucleon system. Employing the CD Bonn NN potential, the solution of the relativistic 3N Faddeev equation for $^3$H shows slightly less binding energy than the corresponding nonrelativistic result. The effect of the Wigner spin rotation on the binding is very small.

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3He Spin-Dependent Cross Sections and Sum Rules

We present a measurement of the spin-dependent cross sections for the \vec{^3He}(\vec{e},e')X} reaction in the quasielastic and resonance regions at four-momentum transfer 0.1 < Q^2< 0.9 GeV^2. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt--Cottingham and extended GDH sum rules for the first time. Impulse approximation and exact three-body Faddeev calculations are also compared to the data in the quasielastic region.

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Relativity and the low energy nd Ay puzzle

We solve the Faddeev equation in an exactly Poincare invariant formulation of the three-nucleon problem. The dynamical input is a relativistic nucleon-nucleon interaction that is exactly on-shell equivalent to the high precision CDBonn NN interaction. S-matrix cluster properties dictate how the two-body dynamics is embedded in the three-nucleon mass operator. We find that for neutron laboratory energies above 20 MeV relativistic effects on Ay are negligible. For energies below 20 MeV dynamical effects lower the nucleon analyzing power maximum slightly by 2% and Wigner rotations lower it further up to 10 % increasing thus disagreement between data and theory. This indicates that three-nucleon forces must provide an even larger increase of the Ay maximum than expected up to now.

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Nucleon-deuteron capture with chiral potentials

Present day chiral nucleon-nucleon potentials up to N3LO and three nucleon forces at N2LO are used to analyze nucleon-deuteron radiative capture at deuteron lab energies below E_d= 100 MeV. The differential cross section and the deuteron analyzing powers A_y(d) and A_{yy} are presented and compared to data. The theoretical predictions are obtained in the momentum-space Faddeev approach using the nuclear electromagnetic current operator with exchange currents introduced via the Siegert theorem. The chiral forces provide the same quality of data description as a combination of the two-nucleon AV18 and the three-nucleon Urbana IX interactions. However, the different parametrizations of the chiral potentials lead to broad bands of predictions.

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A first estimation of chiral four-nucleon force effects in 4He

We estimate four-nucleon force effects between different 4He wave functions by calculating the expectation values of four-nucleon potentials which were recently derived within the framework of chiral effective field theory. We find that the four-nucleon force is attractive for the wave functions with a totally symmetric momentum part. The additional binding energy provided by the long-ranged part of the four-nucleon force is of the order of a few hundred keV.

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Lorentz boosted nucleon-nucleon potential applied to the 3He(e,e'p)pn and 3He(e,e'n)pp processes

We formulate an approximate relativistic framework for an analysis of the 3He(e,e'p)pn and 3He(e,e'n)pp reactions with polarized electrons and 3He in the initial state. Restricting the rescattering series to one term linear in the two-nucleon t-matrix we incorporate various relativistic features when calculating a nuclear current matrix element. These relativistic ingredients encompass the relativistic 3He wave function based on the concept of the Lorentz boosted nucleon-nucleon potential together with the boosted 2N t-matrix, relativistic kinematics and relativistic single-nucleon current operator. This allows us to estimate the magnitude of relativistic effects not included in the standard nonrelativistic approach.

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Relativistic effects in exclusive neutron-deuteron breakup

We extended the study of relativistic effects in neutron-deuteron scattering to the exclusive breakup. To this aim we solved the three-nucleon Faddeev equation including such relativistic features as relativistic kinematics and boost effects at incoming neutron lab. energies E_n^{lab}=65 MeV, 156 MeV and 200 MeV. As dynamical input a relativistic nucleon-nucleon interaction exactly on-shell equivalent to the CD Bonn potential has been used. We found that the magnitude of relativistic effects increases with the incoming neutron energy and, depending on the phase-space region, relativity can increase as well as decrease the nonrelativistic breakup cross section. In some regions of the breakup phase-space dynamical boost effects are important. For a number of measured exclusive cross sections relativity seems to improve the description of data.

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Testing nuclear forces by polarization transfer coefficients in d(\vec p, \vec p)d and d(\vec p,\vec d)p reactions at E^{lab}_p = 22.7 MeV

The proton to proton polarization transfer coefficients K_x^{x'}, K_y^{y'}, K_z^{x'} and the proton to deuteron polarization transfer coefficients K_x^{x'}, K_y^{y'}, K_z^{x'}, K_x^{y'z'}, K_y^{z'z'}, K_z^{y'z'}, K_y^{x'z'} and K_y^{x'x'-y'y'} have been measured in d(\vec p, \vec p)d and d(\vec p, \vec d)p reactions at E^{lab}_p = 22.7 MeV, respectively. The data have been compared to predictions of modern nuclear forces obtained by solving the three-nucleon Faddeev equations in momentum space. Realistic (semi) phenomenological nucleon-nucleon potentials combined with model three-nucleon forces and modern chiral nuclear forces have been used. The AV18, CD Bonn, Nijm I and II nucleon-nucleon interactions have been applied alone or combined with the Tucson-Melbourne 99 three-nucleon force, adjusted separately for each potential to reproduce the triton binding energy. For the AV18 potential also the Urbana IX three-nucleon force have been used. In addition chiral NN potentials in the next-to-leading-order and chiral two- and three-nucleon forces in the next-to-next-to-leading-order have been applied. Only when three-nucleon forces are included a satisfactory description of all data results. For the chiral approach the restriction to the forces in the next-to-leading order is insufficient. Only when going over to the next-to-next-to-leading order one gets a satisfactory description of the data, similar to the one obtained with the (semi) phenomenological forces.

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Resolving the Discrepancy of 135 MeV pd Elastic Scattering Cross Sections and Relativistic Effects

Three precise measurements for elastic pd scattering at 135 MeV/A have been performed with the three different experimental setups. The cross sections are described well by the theoretical predictions based on modern nucleon-nucleon forces combined with three nucleon forces. Relativistic Faddeev calculations show that relativistic effects are restricted to backward angles. This result supports the two measurements recently reported by RIKEN and contradicts the KVI data.

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Selectivity of the Nucleon Induced Deuteron Breakup and Relativistic Effects

Theoretical predictions for the nucleon induced deuteron breakup process based on solutions of the three-nucleon Faddeev equation including such relativistic features as the relativistic kinematics and boost effects are presented. Large changes of the breakup cross section in some complete configurations are found at higher energies. The predicted relativistic effects, which are mostly of dynamical origin, seem to be supported by existing data.

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