Total Muon Capture Rates Research Articles

Total muon-capture rate. Application to11B

A study of the total muon-capture rate in nuclei is presented, with the aid of the impulse and closure approximations and under the assumption that the initial nucleus can be described by a mixing of states in theJ-scheme. The theory is applied to the process of muon capture in11B, with a discussion on the value of the average neutrino momentum.

Study of Transition Rate Renormalization Induced by 2p-2h Ground-State Admixtures

The magnitude of nuclear transition matrix elements calculated in the particle-hole model often must be renormalized to give agreement with experiment. We introduce 2p-2h state admixtures in the ground state (of "closed-shell nuclei") and consider transitions to the usual configuration-mixed p-h states. The resulting renormalized transition matrix elements are, for reasonable choices of the ground-state correlations, in better agreement with experiment. Because proper treatment of the excited states is also required for detailed comparison with experiment in the case of partial transitions, we study the total muon-capture rate using the closure approximation. It is found that introduction of 2p-2h states in the ground state does not remove the theoretical-experimental discrepancy for the total capture rate in $^{16}\mathrm{O}$ if the usual range of values for the "average" neutrino momentum is adopted.

Simple Relation between Cross Sections for Neutrino Scattering and Total Muon-Capture Rates by Nuclei

Simple Relation between Cross Sections for Neutrino Scattering and Total Muon-Capture Rates by Nuclei

Simple Relation between Cross Sections for Neutrino Scattering and Total Muon-Capture Rates by Nuclei

Using the closure approximation, we derive a simple relation between the total forward cross section for elastic scattering of neutrinos by nuclei and the corresponding total muon-capture rates. This relation is in good agreement with previous estimates of neutrino scattering cross sections, but still in disagreement with recent experimental data.

Applications of Current Commutation Relations to Muon Capture and Neutrino (Antineutrino) Reactions in Nuclei

Relations among total muon-capture rates in nuclei and the equal-time commutators of the space and time components of the strangeness-conserving weak hadron current are derived. Using the quark field algebra and the closure approximation, this relation yields a total muon-capture rate in ${\mathrm{He}}^{3}$ of $\ensuremath{\Gamma}({\mathrm{He}}^{3})\ensuremath{\approx}2.36\ifmmode\times\else\texttimes\fi{}{10}^{3}$ ${\mathrm{sec}}^{\ensuremath{-}1}$, in very good agreement with experiment. We demonstrate that application of the gauge field algebra to our relations does not yield a result that can be compared with experiment, since we cannot justify the use of the closure approximation in the context of this algebra. Using the quark field algebra and the closure approximation, similar relations are also derived for the total elastic differential cross section for forward scattering of neutrinos off nuclei.

Simple relation between radiative pion absorption and muon-capture in nuclei

It is shown numerically that for light nuclei with J = 0 +, T = 0 ground state, the ratio of the total radiative 1S pion capture rate Γ(π −) to the total muon capture rate Γ(μ −) is very nearly independent of nuclear structure, depending only on the ratio of squares of pionic and muonic atomic wave functions averaged over the nuclear dimension.

The systematics of muon capture in an independent-particle shell model

The total muon capture rate has been calculated in a closure approximation for a large number of heavy nuclei. The nuclear model chosen is that of A independent particles ( Z protons and N neutrons) in the ground state of an infinite spherical well potential. This model correctly reproduces the low neutrino momentum behavior deduced by Foldy and Walecka but leads to values of the total capture rate in disagreement with experiment. The values predicted for the weak interaction coupling constants assuming reasonable values for the average momentum of the emitted neutrinos are about two-thirds of the conventional values or, if one accepts the conventional coupling constants, the necessary neutrino momentum is found to be about 10% less than one would expect. The possible causes of this and previous discrepancies are discussed, and it is concluded that difficulties associated with nuclear physics (the closure approximation and the choice of a proper shell-model potential and an appropriate average neutrino momentum) are the most likely sources of error. The effect of the radial variation of the muon wave function on the capture rate is examined closely and found to be less than 10% for all nuclei.

Muon capture in 40Ca

The total muon capture rate in 40Ca leading to 40K is calculated in the hole-particle model. For the Goldberger-Treiman value of g P/ g A, the result is only slightly larger than the available experimental value. The influence of second class terms is then considered and the variation of total rate with respect to tensor coupling constant is given.

Total Muon-Capture Rate and the Consistency of Migdal's Theory

Migdal's theory of nuclear structure is recast in the shell-model language, enabling us to show that the excellent agreement with experiment of the theory applied to the total muon-capture rate is obtained by an appreciable symmetry breaking of the Wigner's SU(4) supermultiplet structure contrary to other models where the symmetry seems to be well preserved. Thus, the $\ensuremath{\mu}$-capture result is inconsistent with the dipole photoabsorption and inelastic electron scattering processes reflecting the possible breakdown of the quasiparticle hypothesis.

On the calculation of the total muon capture rates for 6Li and 7Li

The semi-empirical method of Foldy and Walecka to calculate total muon capture rates for double magic nuclei turns out to be generally applicable for nuclei with isospin quantum numbers ( T, T z ) = ( T,− T). Λ μ c ( 6 Li) and Λ μ c ( 7 Li) are calculated with this method. Comparison with experiment leads to the conclusion that the measured value for Λ μ c ( 6 Li) is unreliable.

ON THE TOTAL MUON CAPTURE RATE IN Li6 AND NUCLEAR CLUSTER STRUCTURE

ON THE TOTAL MUON CAPTURE RATE IN Li6 AND NUCLEAR CLUSTER STRUCTURE

On the theory of muon capture by complex nuclei (II)

Results of shell model calculations on total muon capture rates are presented for a number of nuclei. Previous calculations on 16O and 40Ca are extended. It is studied in particular in which way the total capture rates depend on the depth of the finite potential well used for calculating the shell model wave functions. It is found that variations of the well depth, which cause a large variation of the fraction of final neutrons in bound or continuum states, cause only rather small variations in the total capture rates. A study is made of total capture rates in even nuclei with Z = 20 or N = 28 , such as 40Ca, 44Ca, 50Ti, 52Cr, 54Fe. It is argued that the variation of the total square of the nuclear matrix elements for muon capture will be linear with Z and N in a reasonable approximation. The nuclear matrix elements and capture rates are calculated using shell model wave functions, comparing results for infinite and finite potential wells for deriving the wave functions. The results for these nuclei depend on the V or A character of the interaction, but also on details of the nuclear model used, in such a way that it seems difficult to determine a reliable value for the ratio of the V and A coupling constants from such data.

Measurement of the total muon capture rate in He 3

By using a high pressure diffusion cloud chamber the total capture rate for muons in helium-3 was measured to be lambda = exp (2140 plus or minus 200) sec/sup -1/. This result is in agreement with Primakof's calculations done on the basis of Universal Fermi interaction theory. (auth)

On the theory of muon capture by complex nuclei (I)

Various nuclear models and methods of calculation for total muon capture rates by complex nuclei are compared. The statistical model is worked out with improved accuracy for N = Z nuclei. Calculations with a simple shell model are made with and without the use of the closure approximation for wave functions calculated with the following potential wells: harmonic oscillator well, infinite potential well, finite potential well. Various corrections are considered, e.g., the influence of the velocity dependent terms. Numerical results are given for 16O and 40Ca. The various models are in reasonable mutual agreement and the closure approximation turns out to be rather reasonable. The coupling constants derived from the experimental capture rates for 16O and 40Ca agree with each other within 10%, but are about 50% lower than the value required according to a universal Fermi interaction. The deviation from this value may arise from the use of wave functions in our models which are not yet sufficiently realistic.