Bremsstrahlung in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math>Decay

Papenbrock, T.; Bertsch, G. F.

doi:10.1103/physrevlett.80.4141

Cited by 59 publications

(130 citation statements)

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“…[166] has reexamined some of the higher corrections to the energy density of a dilute boson gas; and Ref. [167] has studied pairing in a dilute Fermi system, producing analytical expressions relating the pairing gap, the density, and the energy density to the scattering length. Only exploratory work has so far been carried out regarding the more challenging, higher densities where Q/ℵ > ∼ 1.…”

Section: Many-nucleon Systemsmentioning

confidence: 99%

Effective field theory of nuclear forces

Kolck

1999

Progress in Particle and Nuclear Physics

305

303

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The application of the effective field theory (EFT) method to nuclear systems is reviewed. The roles of degrees of freedom, QCD symmetries, power counting, renormalization, and potentials are discussed. EFTs are constructed for the various energy regimes of relevance in nuclear physics, and are used in systematic expansions to derive nuclear forces in terms of a number of parameters that embody information about QCD dynamics. Two-, three-, and many-nucleon systems, including external probes, are considered. * Commissioned for Prog. Part. Nucl. Phys.

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Section: Many-nucleon Systemsmentioning

confidence: 99%

Effective field theory of nuclear forces

Kolck

1999

Progress in Particle and Nuclear Physics

305

303

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“…Perspectives are certain in study of dynamics of the α-decay with some analysis of the bremsstrahlung [5,10,11], in study of dynamics of tunneling in the α-decay [12,13,14,15], in research of peculiarities of the polarized bremsstrahlung during α-decay and influence of electron shells on it [16], in effect [17] called as Münchhausen effect which increases penetrability of the barrier due to charged-particle emission during its tunneling and which could be interesting for further study of the photon bremsstrahlung during tunneling in the α-decay. However, the fully quantum approach (starting from [18] and then [19,20]) seems to be the most accurate and motivated from the physical point of view in description of emission of photons, to be the richest in study of quantum properties and new effects. Among the fully quantum approaches a model proposed for the first time by Papenbrock and Bertsch in [19] has been developing the most intensively, where wave function of photons is used in the dipole approximation.…”

Section: Introductionmentioning

confidence: 99%

“…However, the fully quantum approach (starting from [18] and then [19,20]) seems to be the most accurate and motivated from the physical point of view in description of emission of photons, to be the richest in study of quantum properties and new effects. Among the fully quantum approaches a model proposed for the first time by Papenbrock and Bertsch in [19] has been developing the most intensively, where wave function of photons is used in the dipole approximation. In such dipole approach the matrix element is calculated with higher convergence and without visible decrease of accuracy, that makes this problem to be studied for many researchers in the fully quantum consideration.…”

Section: Introductionmentioning

confidence: 99%

Multipolar Approach for Description of Bremsstrahlung During α -Decay and Unified Formula of the Bremsstrahlung Probability

Maydanyuk¹

2009

TONPPJ

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Model of angular bremsstrahlung of photons emitted during α-decay is presented. A special emphasis is given on development of unified formalism of matrix elements in the dipole and multipolar approaches. A probability of the emission of photons calculated on the basis of the multipole model without any normalization on experimental data (i. e. in absolute scale) is found at 90• of the angle ϑαγ between directions of motion of the α-particle (with its tunneling under barrier) and emission of photons to be in a good agreement with the newest experimental data for the 210 Po, 214 Po, and 226 Ra nuclei. The spectrum for 244 Cm is found at ϑαγ = 25• to be in satisfactory agreement with high limit of errors of experimental data of Japanese group. A comparative analysis for the spectra calculated for 210 Po by the multipole and dipole approaches in the absolute scale and with normalization on experimental data is performed. The emission of photons from the internal well in the dipole approach is found to be not small while the multipolar approach does not show such a strong dependence. Distribution of the bremsstrahlung probability on the numbers of protons and nucleons of the α-decaying nucleus in selected region close to 210 Po is obtained. An unified formula of the bremsstrahlung probability during the α-decay of arbitrary nucleus expressed directly through the Qα-value and numbers Ap, Zp of nucleons and protons of this nucleus is proposed.

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“…Moreover, Smith and Wilkin [18] proved that these symmetric polynomials are indeed exact eigenstates (see Ref. [19] for an alternative proof). In this note, we point out that the analytic proof by Smith and Wilkin works not only for a delta-function potential but also for an arbitrary potential which possesses translational and rotational symmetries.…”

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confidence: 99%

“…This statement can be easily proved by operatingV on the right hand side of Eq. (19) and by using Eqs. (17) and (23).…”

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confidence: 99%

Exact eigenstates for trapped weakly interacting bosons in two dimensions

Huang

2000

Phys. Rev. A

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A system of N two-dimensional weakly interacting bosons in a harmonic trap is considered. When the two-particle potential is a delta function Smith and Wilkin have analytically proved that the elementary symmetric polynomials of particle coordinates measured from the center of mass are exact eigenstates. In this study, we point out that their proof works equally well for an arbitrary two-particle potential which possesses the translational and rotational symmetries. We find that the interaction energy associated with the eigenstate with angular momentum L is equal to aN (N −1)/2+(b − a) N L/2, where a and b are the interaction energies of two bosons in the lowest-energy one-particle state with zero and one unit of angular momentum, respectively. Additionally, we study briefly the case of attractive quartic interactions. We prove rigorously that the lowest-energy state is the one in which all angular momentum is carried by the center of mass motion. 03.75.Fi,05.30.Jp,67.40.Db The study of Bose-Einstein condensation in trapped atomic gases has attracted a great deal of attention in the past few years [1][2][3][4]. One of the central issues has been the possibility of creating quantized vortices in these dilute atomic gases. Recently, vortex states in various systems have been experimentally observed [5,6]. Some theoretical investigations on quantized vortices and on rotating Bose condensates have also been carried out both in the Thomas-Fermi limit of strong interactions [7][8][9][10] and in the limit of weak interactions [11][12][13][14][15][16][17][18] between the atoms. For the weakly interacting bosons one is naturally led to study the model of N two-dimensional bosons in a harmonic trap with weak repulsive delta-function interactions [11]. One important theoretical problem here is to understand the properties of the system with a given total angular momentum L. Numerical studies have shown that when L > N the lowest-energy state is the one where an array of singly quantized vortices is formed [15,8]. However, due to the complexity of these states, very few analytic results are known. In the range 0 ≤ L ≤ N the structure of lowest-energy states turns out to be simpler. Numerical computations by Bertsch and Papenbrock [13] showed that the interaction energy of the lowest-energy states has a very simple form and decreases linearly with L (the only exception being that for L = 1). They also noted that the wave functions for the lowest-energy states are simply the elementary symmetric polynomials of complex coordinates relative to the center of mass. Very recently, this remarkable formula for interaction energy was derived analytically by Jackson and Kavoulakis [17]. Moreover, Smith and Wilkin [18] proved that these symmetric polynomials are indeed exact eigenstates (see Ref. [19] for an alternative proof). In this note, we point out that the analytic proof by Smith and Wilkin works not only for a delta-function potential but also for an arbitrary potential which possesses translational and rotational symmetri...

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Bremsstrahlung inαDecay

Cited by 59 publications

References 11 publications

Effective field theory of nuclear forces

Effective field theory of nuclear forces

Multipolar Approach for Description of Bremsstrahlung During α -Decay and Unified Formula of the Bremsstrahlung Probability

Exact eigenstates for trapped weakly interacting bosons in two dimensions

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