Nuclear fusion rates from resonant states of 3Hedμ molecular ion

We present new theoretical calculations of nuclear fusion rates λ _f ^J from the resonant states of the muonic molecular ion ³Hedμ ⁺⁺ with total angular momenta J=0,1. As a byproduct, new very accurate variational wave functions for these states have been obtained. Using these wave functions, the probability density |Ψ(R=0)|² in a fusion region has been calculated by extrapolating the variational solution to small internuclear distances by means of the multi-channel adiabatic solution. Calculated fusion rates for the states J=0 and J=1 are: λ _f ⁰ =1.9·10⁵s^-1 and λ _f ¹ =0.65·10³s^-1, respectively. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dynamics of muonic atom cascade in hydrogen-helium mixtures

The deexcitation of excited muonic protium and deuterium in the mixture of hydrogen and helium isotopes is considered. Methods of experimental determination of the probability of direct atomic muon capture by hydrogen and muon transfer rates from excited muonic hydrogen to helium are proposed. Theoretical results for the population of the muonic atoms in the ground state, , are compared with the existing experimental data. Results obtained for mixtures are of interest for investigation of nuclear fusion in muonic molecules. Received: 6 August 1998 / Revised: 1st October 1998 / Accepted: 2 October 1998     

Reaction dynamics of Cl O ClO O

Applying the two photon laser induced fluorescence technique for nascent state resolved ClO() detection, the reaction dynamics of Cl+O ClO+O₂ is investigated. The ClO product is formed in its electronic ground state ClO(). A complete product state analysis in terms of vibration, rotation, spin-orbit and -states indicates that nascent ClO radicals are formed in v =0-6 vibrational states peaking at v =3. The ClO fragment shows a moderate rotational excitation, described by a Boltzmann distribution with a temperature parameter of 1300 K 200 K. The spin orbit ratio of :. Most of the excess energy is released as translational energy or as internal energy of the O₂ product. By comparing our results with the trajectory studies of Farantos and Murrell, we favour a reaction mechanism, where the transition complex is planar containing an essentially linear OOCl group. In order to determine the possible influence of vibrationally excited ClO on other trace components of the atmosphere, especially the reaction ClO(v >0)+ O₃, a rough estimate of the vibrational relaxation rate of ClO with the major atmospheric collision partner, N₂, has been performed. A measurement of the vibrational distribution of ClO at different N₂ pressures indicates a mean vibrational relaxation rate of . Received: 27 February 1998 / Revised: 1st April 1998 / Accepted: 15 April 1998     

Rotational excitation of H2 and N2 molecules by electron impact

The rotational excitation of the H₂ and N₂ molecules from (J→J+2,J=0) and (J→J+2,J=1) states by electron impact is studied, in the framework of the regional-plane-wave approximation. The empirical cut-off parameterρ, involved in these calculations, is varied to give the best fit to the experimental data of Srivastava and co-workers.     

Charge transfer from the ground state of muonic hydrogen to at room temperature

The present status of research of muon transfer from the ground state of muonic protium to ⁴He is reviewed. The analysis of a recent measurement in a triple gas mixture of H₂+⁴He+Ne at 15 bar and room temperature is presented and the result is compared to the existing experimental and theoretical rates. The average muon transfer rate from protium to ⁴He determined from all lifetime measurements is . Received: 22 January 1998 / Revised: 4 March 1998 / Accepted: 31 March 1998     

Isotope dependence of particle-decay rates of muonic molecular ions (d3,4Heμ) J=1 below (dμ)1s-3,4He threshold

Rates of particle-emitting decay of the resonant state of the muonic molecular ion (dHe) _J=1 lying below the (d)_1s-He threshold can decay to the d-He scattering state. The resonant state is estimated by scattering calculations with the non-adiabatic coupled-rearrangement-channel method. Strong isotope dependence of the decay rates of (d³He) _J=1 and (d⁴He) _J=1 is predicted, though the calculated radiative decay rates of the states are almost the same. In (d³He) _J=1, the particle decay width is three times larger than the radiative decay width, while the two types of decay widths are almost the same in (d⁴He) _J=1. This results in a strong hindrance of the branching ratio of the radiative decay of (d³He) _J=1 compared with the case of (d⁴He) _J=1. This is consistent with a recent observation of the radiative decay of the two molecular states.     

Singularity of the specific heat of two-dimensional random Ising models

The singularity of the specific heat is studied for the dilution (J>J'>0) type and Gaussian type random Ising models using the Pfaffian method numerically. The type of singularity at the paramagnetic-ferromagnetic phase boundary is studied using the standard regression method using data up to system size. It is shown that the logarithmic type singularity is more reliable than the double-logarithmic type and cusp type singularities. The critical temperatures are estimated accurately for both the dilution type and Gaussian type random Ising models. A phase diagram relating strength of the randomness and temperature is also presented. Received: 26 February 1998 / Revised: 15 May 1998 / Accepted: 25 June 1998     

Energetical structure of muonic molecular ions ddµ and dtµ

The long-lived states lying below then=2 threshold in muonic molecular ions ddµ and dtµ are reviewed. We have considered all the known long-lived states both of normal and anomalous spatial parity, the bound states as well as resonant three-body states of shape and Feshbach types. It is shown that these states could be satisfactorily classified in terms of the Born-Oppenheimer adiabatic theory. We calculate some characteristic properties of the Feshbach resonances, thus obtaining that the life-time of the 3d states is greater than 10^–11 s, and the fusion rate from these states less than 10⁹ s^–1. The geometry of the 4f(J=0,v=0) state shows that it does not obey approximate ungerade symmetry. On the contrary, the low vibrational 3d states are approximately of gerade symmetry, as a result these states decay ejecting dµ atoms in the same proportion as tµ atoms.     

Temperature dependence of rotational relaxation of methane in the 2ν3 vibrational state by self- and nitrogen-collisions and comparison with line broadening measurements

Depopulation rates of rotational levels in the v₃ = 2 vibrational state of ¹²CH₄ are investigated by a pump-probe technique. Methane molecules are excited into selected rotational levels by tuning the pump laser to 2ν₃ lines. The time evolution in population of the excited level after the pumping pulse is monitored by tuning the probe laser to a (3ν₃ ← 2ν₃) line corresponding to a transition with the excited rotational level as the lower level. Measurements were performed from room temperature down to 100 K in pure CH₄ and in CH₄-N₂ mixtures. The rotational relaxation rate coefficients are given for the J = 1, A₂, J = 1, E, J = 1, F₂ and J = 0, F₂ levels. The results are compared with the available data on line broadening coefficients. The temperature dependence of the data on N₂-broadening is particularly well reproduced by the power law deduced from the results on rotational relaxation.     

General method for the reduction of the effective rotational hamiltonian of molecules. Rational approximants and Padé approximants

A general method for reducing the effective rotational Hamiltonian for moleculesH _rot to the empirically constructed form in the {J_±, J_z} representation (molecules of the asymmetric-top type), applicable to Hamiltonians having improved convergence with nonpolynomial dependence on the angular momentum J, is developed. Rational forms for the reducedHrot and reduced Padé approximants for the rotational energy operator of the molecules are proposed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 32–37, August, 1985.     

How to get access to long range states of highly excited molecules

Due to competition between ionic and covalent dissociation, the excited potential curves of the alkali dimers display long range structures, leading in some cases to secondary wells. We discuss the possibility of populating the well (with a depth of 1614.8 cm^-1, located at R _e = 30.5a ₀ ) that is present in the Na₂ potential curve and propose detection schemes. Received: 28 May 1998 / Revised: 5 August 1998 / Accepted: 24 September 1998     

Determination of the helium-4 mass in a Penning trap

The determination of the rotational quadrupole alignment of diatomic molecules via REMPI detection is investigated. In this process a high focal intensity usually increases the detection probability. At high intensities the AC Stark effect may cause a splitting of the normally degenerate m_J sublevels of a rotational state J beyond the spectral width of the exciting radiation. This leads to a selective detection of only certain m_J states with the consequence that deduced alignment factors can be misleading. From the theoretical considerations line profiles are explicitly calculated for dynamic polarizabilities which represent the B ¹Σ⁺ _u←X ¹Σ⁺ _g transition of H₂, in order to fit an experimental (3+1) REMPI spectrum and to predict (1+1') line shapes as a function of laser intensity. It is further shown that the deduced quadrupole alignment factor A ₀ ⁽²⁾ is significantly changed by the second order AC Stark effect when the intensities are chosen high enough to observe asymmetric broadened line profiles. Different combinations of relative linear polarizations of the exciting and ionizing laser beams are discussed. Received 1st August 2000 and Received in final form 2 May 2001     

Bound state spectra of three-body muonic molecular ions

The results of highly accurate calculations are presented for all twenty-two known bound S(L = 0)-, P(L = 1)-, D(L = 2)- and F(L = 3)-states in the six three-body muonic molecular ions ppμ,pdμ,ptμ,ddμ,dtμ and ttμ. A number of bound state properties of these muonic molecular ions have been determined numerically to high accuracy. The dependence of the total energies of these muonic molecules upon particle masses is considered. We also discuss the current status of muon-catalysis of nuclear fusion reactions.     

The rotational levels of the ground vibrational state of formaldehyde

A variational procedure for rovibrational energy levels and wavefunctions of centrally connected tetra-atomic molecules is extended to include high rotational states, and in particular, J ? 10 levels for the vibrational ground state of formaldehyde. It is very important to do this because it has made possible the calculation of the usual rotational spectroscopic constants which correspond to the forcefield and geometry. A direct comparison with the ‘observed’ spectroscopic constants is therefore possible. The geometry and forcefield are refined against 65 J = 0 levels of H₂CO, 6 J = 0 levels of D₂CO, 42 J = 1, 70 J = 2 and 98 J = 3 levels of the ground and fundamentals of H₂CO and D₂CO, using an iterative scheme. The mean absolute error of the J = 0 levels is 1·10 cm^?1 and that for J ≠ 0 is 0·005 cm^?1, and the predicted geometry is CH = 1·10064 Å, CO = 1·20296 Å and HCO = 121·648°. Finally, the rotational constants A, B, and C for the ground state are 281956, 38846 and 34003 MHz, compared with the observed values 281971, 38836, and 34002 MHz. The centrifugal distortion constants Δ_J , Δ_JK , Δ_K and δ_J , are 77, 1275, 18113 and 11 kHz compared with 75, 1291, 19422 and 10 kHz. These results underline the accuracy of the new quartic forcefield.     

Rotation-vibration energy cluster formation in XH2D and XHD2 molecules (X = Bi, P, and Sb)

We investigate theoretically the energy cluster formation in highly excited rotational states of several pyramidal XH₂D and XHD₂ molecules (X = Bi, P, and Sb) by calculating, in a variational approach, the rotational energy levels in the vibrational ground states of these species for J?70. We show that at high J the calculated energy levels of the di-deuterated species XHD₂ exhibit distinct fourfold cluster patterns highly similar to those observed for H₂X molecules. We conclude from eigenfunction analysis that in the energy cluster states, the XHD₂ molecule rotates about a so-called localization axis which is approximately parallel to one of the X-D bonds. For the mono-deuterated XH₂D isotopologues, the rotational spectra are found to have a simple rigid-rotor structure with twofold clusters.     

Narrow α + <Superscript>28</Superscript>Si elastic-scattering states at high excitation in <Superscript>32</Superscript>S

The excitation function and angular distributions of elastic α-particle scattering on ²⁸Si have been measured in the laboratory energy range 6-28 MeV using a backscattering technique on a thick target, yielding a continuous energy distribution. More than 200 narrow states are observed, with widths in the range ∼ 30-100 keV at excitation energies E ^* = 13-32 MeV. Angular distributions at backward angles were measured, and angular momentum values of more than 83 states have been deduced. The analysis gives spin-parities J ^π, α-partial widths Γ_α and reduced widths of the narrow high-lying resonant states in ³²S. The experimentally observed states display both the negative- and the positive-parity rotational-like sequences with seemingly no parity splitting, a finding which is at variance with most potential-model predictions. The deduced effective moment of inertia indicates a more extended structure than the ground-state configuration. The observed strength of each ℓ-value is analyzed in terms of an underlying split doorway state of Lorentzian form, which yields an interpretation as fragmented rotational α + ²⁸Si states. Received: 26 June 2000 / Accepted: 16 September 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: kkallman@abo.fi RID="b" ID="b"Present address: Swedish Polytechnic, FIN-65200 Vasa, Finland. Communicated by D. Guerreau     

Fermionic Ising glasses with BCS pairing interaction. Tricritical behaviour

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T-g plane, where g is the strength of the pairing interaction, for fixed variance J ² /N of the random couplings J_ij, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line g=g _c (T) that ends at a tricritical point T ₃ =0.9807J, g ₃ =5,8843J, from where it becomes a first order transition line that meets the line of second order transitions at T _c =0.9570J that separates the NP and the SG phases. For T<T _c the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in . Received 14 May 1998     

Calculations of the Auger deexcitation rate of the dtμ within the muonic quasi-molecule, [(dtμ)dee]

A key process in muon catalysed fusion is the deexcitation of the dt within the resonant muonic quasi-molecule [(dt)dee], by emission of an Auger electron. The dt in the quasi-molecule is initially in a weakly bound excited state withJ=1 andv=1. In this paper, calculations taking full account of the molecular nature of the quasi-molecule are carried out of the rate of the dominant deexcitation to the state withJ=0 andv=1.     

Reflection of cold atoms from an array of current-carrying wires

We report the realization of a new type of magnetostatic mirror for slowly moving atoms which comprises a planar array of parallel wires alternately carrying electric current in opposite directions. One of the features of this atomic mirror is that the magnetic field may be readily varied, switched or modulated by altering the current in the wires. Reflection signals close to 100% at a pulsed current of 3 A are demonstrated for a beam of free-falling laser-cooled cesium atoms at normal incidence. The current dependence of the reflection signals exhibits structure which is associated with the sequential onset of reflection of cesium 6² S _1/2 , F=4 atoms in the m=+4, +3, +2 and +1 magnetic states. Measurements of the spatial distribution of the reflected atoms indicate the reflection is predominantly specular at currents of 3 A. Received: 31 August 1998 / Accepted: 6 October 1998     

Dissociative excitation of the fluoromethanes by electron impact

Emission spectra following electron impact on molecules of the homologous series of fluoromethanes CH_xF_4-x with x=0-4 have been investigated from the near infrared at 700 nm to the ultraviolet VUV-spectral region at 100 nm. Earlier experimental data for the visible and ultraviolet spectral region were revised and evaluated again on the basis of reliable new data for the dynamic viscosity of the molecules. The measurement of absolute and relative cross-sections were systematically extended into the VUV region from 100 nm to 200 nm. The examination of atomic lines as well as molecular band systems in the VUV gives further insight into the dissociation mechanism and shows that many excited levels even of atomic and molecular species cannot be populated directly, but only by transitions from higher-lying energy levels. Simple steric effects can be distinguished from more complex transition phenomena. Received: 25 February 1998 / Revised: 29 May 1998 and 18 June 1998 / Accepted: 23 June 1998