The equivalent photon approximation for coherent processes at colliders

We consider coherent electromagnetic processes for colliders with short bunches, in particular the coherent bremsstrahlung (CBS). CBS is the radiation of one bunch particles in the collective field of the oncoming bunch. It can be a potential tool for optimizing collisions and for measuring beam parameters. A new simple and transparent method to calculate CBS is presented based on the equivalent photon approximation for this collective field. The results are applied to theφ-factoryDAΦNE. For this collider about 5·10¹⁴ d E _γ/E _γ photons per second are expected in the photon energyE _γ range from the visible light up to 25 eV.     

The equivalent photon approximation for coherent processes at colliders

We consider coherent electromagnetic processes for colliders with short bunches, in particular the coherent bremsstrahlung (CBS). CBS is the radiation of one bunch particles in the collective field of the oncoming bunch. It can be a potential tool for optimizing collisions and for measuring beam parameters. A new simple and transparent method to calculate CBS is presented based on the equivalent photon approximation for this collective field. The results are applied to the??-factoryDA??NE. For this collider about 5·10¹⁴ d E _??/E _?? photons per second are expected in the photon energyE _?? range from the visible light up to 25 eV.     

The equivalent photon approximation for coherent processes at colliders

We consider coherent electromagnetic processes for colliders with short bunches, in particular the coherent bremsstrahlung (CBS). CBS is the radiation of one bunch particles in the collective field of the oncoming bunch. It can be a potential tool for optimizing collisions and for measuring beam parameters. A new simple and transparent method to calculate CBS is presented based on the equivalent photon approximation for this collective field. The results are applied to theφ-factoryDAΦNE. For this collider about 5·10¹⁴ d E _γ/E _γ photons per second are expected in the photon energyE _γ range from the visible light up to 25 eV.     

Application of the “electronic bridge” theory to some highly converted nuclear transitions

The influence of the atomic electron cloud on the gamma decay constantλ _γ was evaluated in third-order approximation according to the theory of Krutov for some highly converted nuclear transitions (resonance case only). The results areλ _γ ⁽³⁾ =1.5×10⁵ λ _γ ⁽³⁾ for the 73 eV transition of U-235m andλ _γ ⁽³⁾ =1.01λ _γ ⁽¹⁾ for the 2.17 keV transition of Tc-99m. Values calculated forZ=80,E _γ =2 keV are in good agreement with those of Krutov. Experimental evidence of the calculated effects does not seem to be obtainable at present because of the extremely low gamma intensity of the transitions in question.     

The photodisintegration of6Li and7Li

The photodisintegration of the stable Lithium isotopes has been investigated by spectroscopy of the emitted charged particles using the Giessen bremsstrahlung facility. Protons, deuterons, tritons,³He and alpha particles were detected and identified up to 20MeV particle energy. Angular distributions were measured using γ-ray energies up toE _γ =50 MeV. They are compared with theoretical predictions and with other experiments. A remarkable low (γ, t)-cross section was found for both isotopes in disagreement to previous measurements using virtual photons. Coincidence measurements between the emitted particles were performed in order to study the manybody-breakups of⁷Li.     

Finite-N fluctuation formulas for random matrices

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic Σ _j ^N =1 (x _j ? 〈x〉) is computed exactly and shown to satisfy a central limit theorem asN → ∞. For the circular random matrix ensemble the p.d.f.’s for the statistics ½Σ _j ^N =1 (θ _j ?π) and ? Σ _j ^N =1 log 2 |sinθ _j/2| are calculated exactly by using a constant term identity from the theory of the Selberg integral, and are also shown to satisfy a central limit theorem asN → ∞.     

Angular correlation measurement in the B11(d,pγ)B12 reaction

Thep-γ angular correlations in B¹¹(d, p)B¹² reaction have been measured in both reaction and azimuthal planes for proton angles 35° at E_D=1.60 and 2.40 MeV. The correlation coefficient A ₂ ⁰ and the distortion parameterλ were calculated. The obtained values of the shift of the symmetry axis from the recoil direction, Φ₀ and the parameterλ are far from there plane wave limits. The anisotropy of the angular correlation gives two possible values, 1⁺ and 2⁺, for the spin of the first excited state of B¹².     

E2 andE3 transition strengths in some rare-earth nuclei

Coulomb excitation byα-particles of vibrational-like states in even-mass rare-earth nuclei is used to determine the reduced transition probabilitiesB(E2; 0 _gs ⁺ →2 _γ ⁺ ),B(E2; 0 _gs ⁺ →2 _β ⁺ ),B(E2; 2 _gs ⁺ →0 _β ⁺ ) andB(E2; 0 _gs ⁺ →3 _oct ^? ) in¹⁵⁰Nd,^{152, 154}Sm,^{154, 158}Gd,¹⁶⁴Dy and¹⁶⁶Er. TheB(Eλ; 0 _gs ⁺ →I=λ)-values range from 2.4 to 6.5 single-particle units for transitions to the 2 _γ ⁺ -states, 0.8 single-particle units for the 2 _β ⁺ -states and from 14.1 to 21.7 single-particle units for the 3^?-states.     

IsoscalarE2 transition strengths in 10≦A≦48 nuclei

Electric quadrupole transition strengths for the 2 ₁ ⁺ ,T=1→0 ₁ ⁺ ,T=1γ-decay branches are summarized for 10≦A≦42 nuclei. In¹⁰B the corresponding branch has been remeasured by use of the⁹Be(p, γ)¹⁰B resonance reaction atE _p =320 keV; an upper limit of 0.6% is found. The variation of theE2 strengths within each individualT=1 isobaric multiplet reveals the particleor hole-character of the levels involved. The isoscalar 2 ₁ ⁺ →0 ₁ ⁺ transition strengths in 10≦A≦48 nuclei vary between 2 and 20 Weißkopf units showing drastic shell effects. Results for the ratio of neutron and proton matrix elements deduced from analogγ-decay studies and from inelastic pion scattering are compared.     

On the mechanism of formation of excited states of the 8Be nucleus in the reaction 12C(γ, 3α)

The reaction ¹²C(γ, 3α) was studied with the aid of a diffusion chamber placed in a magnetic field, filled with a methane-helium mixture, and irradiated with bremsstrahlung photons of endpoint energy 150 MeV. The total reaction cross section was measured in the energy range E _γ < 40 MeV. The ground state; the first, second, and unseparated third and fourth excited states; and highly excited states (in the range 19.9 < E _x < 25.2 MeV) of the ⁸Be nucleus manifested themselves in the distribution of events with respect to the energy of the relative motion of two alpha particles. A resonance that is characterized by the energy of E₀ = 0.72 MeV and the width of Γ = 0.80 MeV and which was identified as a ghost anomaly was found between the ground state and the first excited state. Partial cross sections were measured for various channels. Excited states are formed in narrow photon-energy intervals, and their partial cross sections are of a resonance shape. It is found that the energy corresponding to the maximum of the partial cross section for the ith level, E _m ⁱ , and the excitation energy of the next level, E ₀ ⁱ⁺¹ , are correlated: E _m ⁱ = E ₀ ⁱ⁺¹ + ?, where ? is the reaction threshold. The results are qualitatively explained on the basis of a model that assumes photon absorption by an alpha-particle pair.     

The potential for which E n 1 ′ 12=E n 2 ′ l1 in nonrelativistic quantum mechanics

The answer is provided to the question ‘What is the potential for which E _{n 1} ^′ l₂=E _{n 2} ^′ l₁ in nonrelativistic Quantum Mechanics?’     

Stimulated multiphoton emission from exciton Bose condensate

The coherent recombination of several (N) Bose-condensed excitons with simultaneous creation of N photons is considered. Due to the momentum conservation law, the total momentum of created photons is zero because of the zero momentum of excitons in Bose condensate. This requirement, in conjunction with the fact that the photon wavenumbers are fixed and equal to approximately E _g /c (E _g is the semiconductor gap and c is the speed of light), determines the mutual orientation of the wavevectors of emitted photons. This can be seen from the photon angular correlation in the experiments with several appropriately oriented detectors operating in the time-coincidence mode. It is shown that, if these processes are induced by N? 1 external laser beams (each with wavevector k _i ), then a unidirectional radiation with recoil wavevector k=?∑_i k _i should emerge from the exciton system. The intensities of coherent three-and four-exciton recombination are estimated for the exciton system in Cu₂O.     

Nuclear orientation study of97, 103, 105Ru in Fe

Angular distributions have been measured forγ-rays emitted following the decays of^{97, 103, 105}Ru oriented in an iron matrix at temperatures down to 2.8mK. From the temperature dependence of theγ-anisotropies the magnetic hyperfine splitting frequenciesν _M =|gμ _N B _HF/h| of^{97, 103, 105}RuFe were found to be 110(7), 57(15) and 80 _?50 ⁺¹⁷ MHz, respectively. With the known hyperfine fieldB _HF=?489.6(4.0) kG the nuclearg-factors are derived as ∣g(⁹⁷Ru;j ^π=5/2⁺)∣=0.29(2), ∣g(¹⁰³Ru;j ^π=3/2⁺)∣=0.15(4) and ∣g(¹⁰⁵Ru;j ^π=3/2⁺)∣=0.21 _-0.13 ^+0.05 . The analysis for¹⁰³RuFe has been performed with the assumption ofj ^π=3/2⁺ and 5/2⁺ for the ground state of¹⁰³Ru. Taking into account experimentally knowng-factors of 3/2⁺ and 5/2⁺ states in this mass region, our data strongly favour the assignmentj ^π=3/2⁺ for the¹⁰³Ru ground state.     

Recurrence of random walks in the Ising spins

Consider the 1/2-Ising model inZ ². Let σ _j be the spin at the site (j, 0)∈Z ² (j=0, ±1, ±2, ...). Let \(\{ X_n \} _{n = 0}^{ + \infty } \) be a random walk with the random transition probabilities such that $$P(X_{n + 1} = j \pm 1|X_n = j) = p_j^ \pm \equiv 1/2 \pm v(\sigma _j - \mu )/2$$ We show a case whereE[p _j ⁺ ≧E[p _j ^? ], but \(\mathop {\lim }\limits_{n \to \infty } X_n = - \infty \) is recurrent a.s.     

Orthopositronium decay into axions

We point out that if the mass of the hypothetical particle called the axion is less than 2m_e, then it can be emitted in the decay of orthopositronium. The lifetime of the decay 1³S₁ → γh is calculated to be about 8 s. We suggest an experiment to look for “single” photons from positronium annihilation. An accurate measurement of the energy E_γ of these photons gives the mass of the axion through the relation m²_axion = 4m_e(m_e ? E_γ).     

Time delay measurements in a low-energy nuclear reaction from a bremsstrahlung experiment

We report the observed spectra of low-energy γ-rays emitted in the elastic scattering p + ¹²C at E_p = 1975 and 1985 keV. The phase difference between the two amplitudes of bremsstrahlung emitted before and after the formation of a nuclear intermediate state has been extracted. This phase difference has been interpreted in terms of the reaction time delay.     

Perturbation theory with a tridiagonal zeroth-order hamiltonian

We generalize the Rayleigh-Schrödinger perturbation formalism to the hamiltonians H=H₀+λH₁ where the correction λH₁ is small and the unperturbed operator H₀ is represented by an infinite tridiagonal matrix. This enables us to construct the solutions E=E₀+λE₁+λ²E₂+… and |ψ〉 = |ψ₀〉+λ|ψ₁〉+λ²|ψ₂〉+… in terms of the analytic continued fractions.     

A dispersion analysis of pion photoproduction from nucleons. II

The paper gives an account of numerical results forl=0 andl=1 multipole amplitudes of pion photoproduction. They have been obtained by solving integral equations which originate from fixed angle dispersion relations that have been deduced in an earlier paper. In this Part II presented are solutions of truncated integral equations for photoproduction amplitudes, which take into account coupling with the most important transitionsM ₁₊ ⁽³⁾ (in the isovector case) andE ₀₊ ⁽⁰⁾ (in the isoscalar case). Discussed are implications of such an approach and a comparison of results obtained by a different method is being made.     

Nuclear structure effect on internal conversion ofl-forbidden transitions in139La,141Pr and203Tl

Accurate experimental internal conversion data have been used to study the effect of nuclear penetration in the case of thel-forbidden transitions in¹³⁹La (165.8 keV),¹⁴¹Pr (145.4 keV) and²⁰³Tl (279.2 keV). The nuclear penetration parameterλ and theE2/M 1 mixing ratioδ ² have been deduced by graphical analysis. Following results were obtained:λ=2.8±1.3,δ ² =(8.4 _?8.4 ^+14.0 )·10^?4 for¹³⁹La,λ=1.2±0.6,δ ²=(4.8±0.5)·10^?3 for¹⁴¹Pr, andλ=6.4±1.1,δ ²=1.36±0.12 for²⁰³Tl.     

Energieverteilung und Wirkungsquerschnitt der Photoprotonen aus N15

The energy spectra of photo protons from highly enriched N¹⁵ were investigated with the bremsstrahlung from the Heidelberg betatron running at six different endpoint energies between 19 and 30.5 MeV. The protons were detected at 90° to theγ-beam by means of a CsJ-spectrometer with pulse shape discrimination. The energy spectra show pronounced maxima atE _p =3.2; 4.6; 9.5 and 13.3 MeV. Proton yields are given as a function of endpoint energy, the yield value atE ₀=30.5 MeV being (7.0±0.8) μb/MeV · ster. Because the first excited state in the daughter nucleus C¹⁴ lies 6.09 MeV above the groundstate, the cross section for groundstate transitions of the process N¹⁵(γ, p)C¹⁴ could be derived from the upper 6 MeV of the single proton spectra. The main contribution to the cross section comes from the region between 18 and 26 MeV excitation energy with maxima at 19.5; 20.4; 22.7 and 24.5 MeV. A “pygmy resonance” occurs at 15.2 MeV with further less pronounced structures at 13.6 and 17.0 MeV. The integrated cross section for groundstate transitions up to 30.5 MeV is (22±3) MeVmb assuming isotropic angular distribution. The ratios of protons from transitions to excited states and from the (γ, n p)-reaction to those of groundstate transitions rise from 0.45 atE ₀=24.5 MeV to 0.70 atE ₀=30.5 MeV.