Coupling Constant Of Interaction Research Articles

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.

A spontaneous symmetry-breaking model for baryon spectrum

We examine a Yukawa-type interaction of the baryon and meson octets looking for a non-symmetrical solution of the Dyson-Schwinger equations for the Green functions. The baryon masses are calculated in the framework of the model. The Σ and Λ masses turn out to be different, and our model accounts for the octet enhancement. To fix the numerical values we used the experimental value of the nucleon — pion interaction coupling constant, the average mass of baryons and one more masslike parameter. A good agreement with known baryon masses is obtained.

The effective superconducting hamiltonian for alloys with magnetic impurities

It is shown that, in alloys containing magnetic impurities, the effective coupling constant of the BCS interaction is changed by terms proportional to the concentration of impurities when the Anderson Hamiltonian is transformed into an antiferromagnetic exchange interaction between the impurity spins and the conduction electrons.

Protonenrelaxation in Mn2+‐Lösungen, Einfluß der Hyperfeinkopplung. II. Experimente

AbstractA spectrometer is described allowing the measurement of transverse relaxation times ≳ 30 ms at 40 kc/s and of longitudinal relaxation times ≳ 0,1 s within the range of 40 kc/s to 1 Mc/s at any frequency. The relative large sample volume of 800 cm3 and the premagnetisation of the sample in a strong magnetic field (⩽ 800 Oe) assure a sufficient signal intensity.The longitudinal proton relaxation time in aqueous solutions of Mn2+‐ions determined in a temperature range of 15…95°C at frequencies between 15 kc/s and 1 Mc/s indicates an important influence of the hyperfine coupling. The experimental results are in good agreement with the result of the calculations of SAMES and MICHEL in Part I of this paper. The doubling of electron relaxation time and the decrease of scalar contribution of the relaxation rates for high temperatures during passing from high to low fields is evident. Furthermore, the theoretically predicted large range of validity of the weak field formula which describes the experimental results up to 1 Mc/s is noteworthy. However, it is not possible to give a reasonable interpretation of the experimental results by means of the theory of Solomon and Bloembergen.From the experimental results the till now always assumed temperature independence of the coupling constant of the scalar interaction in aqueous solutions of Mn2+‐ions could clearly be proved between 0 and 100°C.Studies on solutions of Mn2+‐ions in formic acid and methanol, respectively, show that the dipole contribution of the relaxation rates for sufficient long correlation times will be also affected by the hyperfine coupling during passing from high to weak magnetic fields.

NMR Studies of a Series of Iron (III) Dithiocarbamate Complexes

The temperature dependence of the proton NMR spectra of a series of iron (III) dithiocarbamates can be interpreted on a model with an iron atom in an intermediate crystal field of octahedral symmetry. The hyperfine interaction coupling constants for the various protons in the 6A1 state arise from d-electron delocalization through the ligands.

Astrophysical evidence for the direct electron-neutrino weak interaction

Observational evidence exists that the central stars of planetary nebulae are evolving into white dwarfs. However, a “gap” in the stellar population appears between the faintest central stars (100 L ⊙ ) and the brightest white dwarfs (1 L ⊙ ). Theoretical models of superluminous white dwarfs (Gap stars) are constructed with and without the inclusion of neutrino emission processes. It is known from previous work that neutrino emission speeds up the evolution of a star. The particular process of importance here is the plasma neutrino process of Adams, Ruderman, and Woo, which depends critically on the existence of the ( eν e )( eν e ) interaction. We have found that the evolution of stars in the mass range 0.7 M ⊙ to 1.1 M ⊙ (Chandrasekhar mass limit for white dwarfs = 1.4 M ⊙ ) is accelerated by a factor of 10 to 100, depending on the assumed chemical composition, if plasma neutrino emission is included; below 0.4 M ⊙ , neutrino emission is unimportant. The more massive Gap stars may be identified observationally on the basis of their very blue color. An upper limit to their evolution time is then obtained from a variety of observational arguments; this upper limit is 5 × 10 5 years, to be compared with the theoretical lifetimes of 2 × 10 5 years with neutrino emission and 2 × 10 6 years without it. From these results we can draw the following conclusions: (1) the presently known rate of plasma neutrino energy loss roughly reproduces the astronomical data; (2) the weak interaction coupling constant for the ( eν e )( eν e ) interaction has a lower limit close to the currently accepted value. Further evidence from the known observational lifetime of central stars and from some crude stellar models indicates that neutrino emission (photoneutrino process) may also be accelerating evolution in the central stars.

Decays of Light Double Hypernuclei and the Four-Baryon Weak Interactions

give us a valuable information on the weak interaction. The relations between the coupling constants of the four-baryon weak interactions are derived from the data for the one-lambda hypernuclei in the framework of the su (3) symmetry model, and the cancellation of the coupling constants for l=O pointed out by Block and Dalitz is compatible with the model. and that AAHe 6 is also stable. It is. desired that some evidences of them are obtained, because the light double hypernuclei are convenient for the analysis. The double hypernuclei are identified by their decay modes. In this paper, the branching ratios for the decays r

Bootstrap Mechanism and Symmetries of Strong Interactions

It is discussed what kinds of symmetries are consistent with the bootstrap mechanism in the baryon-pseucloscalar meson scattering problem. There, the one baryon exchange ap­ proximation is used. The masses of baryons ancl their coupling constants are calculated numerically. The global-, the cosmic- and the G 2-symmetrie;, are allowable, hut the 5'U(3) symmetry is excluded. ~ l. lntroduction Recently some authors 1 l have shown that the bootstrap mechanism predicts such a relation between the coupling constants of the strong interactions that is equal to the one of the octet scheme. The purpose of this article is twofold. We confirm Okabayashi's conjecture about the symmetry character imposed by the bootstrap mechanism on one hand, and on the other hand calculate the masses . of concerned bound states and coupling constants of strong interactions. As to the first problem, rr. Okabayashi 2 l pointed out that the bootstrap -mechanism introduces equalities between the coupling constants in the s-channel and the ones in the t (or u) -channel, and that the equalities give a kind of symmetry character of the strong interactions, which is not always represented by a group, in general. For instance, in Cutkosky's example, this symmetry character inevitably imposes the octet scheme, because he assumed a group character with the eight-dimensional representation and the tri-linear form of the interaction of the eight-component vector field beforehand. These assumptions are sufficient to restrict the symmetry to SU (3) among the groups which include the group of the charge independence. In other words, the equalities imposed by the bootstrap mechanism are accidentally fitted for the assumptions. In ~ 3, the conjecture mentioned above will be confirmed in the baryon-pseudoscalar meson scattering process, and it will be shown that the global symmetry, the cosmic symmetry, the G2 symmetry and the SU (3) symmetry accompanied with the R symmetry are consistent with the bootstrap mechanism, up to this step. The second problem is not so clear. Namely, there may not be any solu­ tion or there may be redundant solutions. Really, in the case of SU (3) sym­ metry there is an undesirable solution. As an example of the calculation of the bound states in a bootstrap mechanism, we have the calculation of the mass

Magnetic Hyperfine Structure of the J=3, K=2 Line of N14H3

The magnetic hyperfine structure of the J =3, K =2 line in the inversion spectrum of N 14 H 3 has been studied by means of a molecular beam maser spectrometer. The results are analyzed by assuming ( I · J ) type inter-actions of the protons and nitrogen spins, and by taking the coupling scheme of angular momenta F 2 = I + J , F = I N + F 2 . The observed hyperfine structure shows two satellite lines on each side of the central line, corresponding to the transitions with Δ F 2 =0, Δ F =±1, and Δ F 2 = Δ F =±1. From the frequency measurements of these satellite lines the coupling constants of the ( I · J ) interactions are determined to be -17.67±0.3 kc for the protons, and 6.73±0.04 kc for the nitrogen nucleus. The theory predicts that the hyperfine components with Δ F 2 =0, Δ F =±1 consist of two groups of lines separated by abut 7 kc, while the experiments show that the separation is smaller than 4.5±0.5 kc. Effects of other types of interactions are taken into consideraction, but they give no appropriat...

On the hypothesis of the variation of the gravitational constant, and on some of its consequences

While the constancy of e 2 h ̵ c and of the coupling constants of strong interactions seems to be essential for the consistency of general relativity, there are not equally cogent reasons for ruling out a variation of the gravitational constant k. We consider, in particular, the hypothesis that k varies according to a law k=k 0[1+a(v/c 2)], where a is a constant of the order of unity, and V is the gravitational potential. The observation of white dwarfs within galactic clusters could provide a test of the hypothesis. We point out further that the problem connected with the existence of a critical mass for neutron stars may perhaps be solved by using the same hypothesis.

THE SPIN WAVE THEORY OF FERROMAGNETIC ANISOTROPY IN CUBIC CRYSTALS

摘要 本文研究了金属极性模型理论中立方铁磁体的d电子之间各向异性相互作用的可能形式,并根据Dyson的自旋波相互作用理论用统计微扰论的方法计算了它们对磁各向异性常数K1(T)的贡献。计算进行到T4的项,在计算中保留到各向异性作用常数的一次方。所得到的K1(T)的温度依赖关系,在理论适用的温度范围内,基本上正比于自发磁化强度的10次方。 Abstract The possible forms of the anisotropic interactions between d electrons in cubic ferro-magnets in the theory of the polar model of metals are studied. Their contributions to the magnetic anisotropic constant K1(T) are calculated based on Dyson's theory of spin wave interactions with the method of the statistical perturbation theory. The accuracy of the calculation is restricted to the first order of the coupling constants of anisotropic interactions, and the results are given up to the T4 terms. It is shown that K1(T) varies roughly as the tenth power of the spontaneous magnetization in the temperature range where the theory is reasonable. 作者及机构信息 邝宇平2, 翁世浚1 (1)华东师范大学物理系; (2)兰州大学物理系 Authors and contacts KUANG YU-PING2, WENG SHI-CHUN1 (1)华东师范大学物理系; (2)兰州大学物理系 参考文献 [1] 施引文献

Bound State Problem and the Determination of Coupling Constants

.In the S-matrix theory of Tomonaga and Schwinger, all particles are re­ garded as elementary and their masses and coupling constants are arbitrary parameters which can be determined only by experiment. However, if ·some particles are composite states of the others, not all of the constants are inde­ pendent and there are relations among them. . Several attempts have been made along this line to determine the coupling constants of the strong interactions ((1)-(4)) . In order to determine whether a particle is elementary or composite it is convenient to consider off-the-mass-shell Smatrix elements such as the form factors or the propagators. The structure of the particle IS reflected in the wave function renormalization Z. Z, being the probability of finding the bare particle, vanishes for a composite particle. In this paper we discuss how the coupling constants among strongly inter­ acting particles can be determined from this condition. In § 2 we explain our method in terms of a simple model neglecting spin structure. In § 3 we treat the case of the pion-nucleon interaction as an actual example. W ealso discuss the problem of subtraction. To take into account left-hand singularity, we make use of the N / D method ~f Chew and Mandelstam.5) In § 4 we calculate the pion-nucleon coupling constant by the Born approximation. All integrals are convergent.

On the Coupling Constants of Strong Interactions

The coupling constants of strong interactions are given by considering Y* 's and other experimental results which include E. It is shown that Y 1* (1385 Mev), Yo* (1405 Mev) and Y 2* (1550 Mev) can be regarded as analogues of N3*' the (3-3) resonance. If the spin-parity of Yo* is P S/ 2 , it may be concluded that gL-,.. ~O, g~l'7t=,g't'\-7 sults and the analysis of other experimental data including E, we shall get a possible scheme on the types and the strengths of

On the Anomalous Threshold and Composite Particles

Using the equal-time Bethe-Salpeter amplitude, the form factor of the charge distribution of composite particles and its threshold are shown to be closely related to those given by the phenomenological quantum field theory. When the Bethe-Salpeter amplitude describes a bound state, its normalization condition can be used to determine the effective coupling constants of interactions between the composite particle and its constituents. In this way, a relation can be derived among the effective coupling constants, even if no detailed information is possessed on the force binding the constituent particles. To examine this relation in experiments gives a way for judging whether the particles are composite or not.

Preliminary determination of Σ-Λ parity using polology

A convenient expression for the normalization of theT-matrix pole term is given. The method of polology is applied to various processes. The coupling constant of theNΛK interaction is determined from the\(\bar p + p \to \Lambda + \bar \Lambda \) angular distribution. Further application of the method to Σ0-K0 production from π−-p interactions and Σ−+π+ production from K−+p interactions indicate that the Σ-Λ relative parity is even, although this conclusion cannot be considered firm. This constitutes support for the hypothesis of global symmetry. Some additional applications of polology are suggested and discussed.

Resonance Model ofΛ−K0Production

A resonance model is proposed to explain the excitation function, the angular distribution, and the large polarization of A in the reaction p + pi / sup -/ yields LAMBDA + K/sup 0/. It is assumed that there exists a low angular momentum resorunce in the channel p + pi /sup -/ yields (resonant state) yields LAMBDA + K/sup 0/. There are five real parameters in this model. Two of these are the coupling constants of the usual interactions. The other three are the position, half-width, and height of the assumed resonance. With reasonable choices of parameters a fairly good fit is obtained, for both a scalar and a pseudoscalar K meson, to the experimental data in the interval 910 to 1300 Mev of the pion kinetic energy in the laboratory system. (auth)

On the observability of the signs of the strong interaction coupling constants

Criteria are given for the observability of the signs of coupling constants appearing in elementary particle interactions. The results are applied to particular strong interaction Lagrangians. For a commonly considered meson-baryon interaction with eight coupling constants, it is shown that only four (independent) relative signs are observable. The signs of the coupling constants in certain meson-meson interactions are discussed briefly. Some difficulties in measuring the observable signs are mentioned.

Environmental perturbations on foreign atoms and molecules in solid argon, krypton and xenon

Perturbations which are responsible for the shifts of electronic and vibrational spectra of species trapped in a solid are considered in terms of the intermolecular potential which describes interactions between these species and neighbouring atoms. It is shown that in certain instances London's theory can give an adequate approximation to the dispersion energy between an electronically excited species and a rare gas atom. The experimental shifts in the electronic absorption spectra of Hg, NH and C2 at lattice sites in rare gas crystals at 4·2°k are explained quantitatively on the basis of a Lennard-Jones (6-12) or (6-8-12) potential between the trapped species and the rare gas atoms. The theory does not adequately explain the shifts in those cases where strong angular dependent forces differing appreciably in the two electronic states are present, data on trapped NH2 free radicals being presented as a case in point. The interaction of sodium atoms with argon at 4·2°k is very complex, the data being consistent with multiple trapping sites for the atoms, a large repulsive interaction between the excited state of sodium and the rare gas, and apparent removal of the three-fold orbital degeneracy in the excited state by the environmental perturbation. The three-fold orbital degeneracy in the 3P1 state of mercury was found also to be removed. The blue shift of 1281 cm-1 for the 3P1 ← 1S0 transition of mercury in solid argon at 4·2°k corresponds almost exactly with the position of one of the two prominent features in the spectrum of mercury in argon gas at comparable densities and illustrates the similarity of structure in the two physical states. The interesting perturbations on the vibrational states of NH and C2 suggest a close similarity to the effect which causes environmental variations of coupling constants for hyperfine interactions in trapped hydrogen atoms.

Parity of theKMeson and theΛBeta-Decay Branching Ratio

The related problems of LAMBDA A beta decay and K/sub mu 2/ decay (via a LAMBDA -antiproton loop) are studied. Dispersion techniques are used to calculate the vector (axial vector) Fermi interaction coupling constant from the known K/sub mu 2/ lifetime and reasonable values of the strong coupling constant for the scalar (pseudoscalar) K case. Each weak coupling constant is then used to place a lower limit on the A beta-decay branching ratio with the result that the limit with a pseudoscalar K is more than one order of magnitude smaller than that with a scalar K meson. The experimental information is essentially consistent with either K parity, for the observed branching ratio is approximately equal to the lower limit predicted for the scalar K case. (auth) The partial lifetime of K yields mu + nu is calculated by dispersion techniques assuming that the K meson is pseudoscalar and that the relevant Fermi interactions arc of the V-A type. The results are compared with experiments and it is concluded that the renormalized axial vector coupling which is responsible for the leptonic decay of hyperons is much smaller than the usual universal Fermi interaction. (auth)

A Model of Strong Interactions

A model of strong interactions is discussed. We divide strong interactions into two classes: the very strong global interactions and the moderately strong charge independent interactions. Most of our discussions are given for the global interactions. Our aim is to transfer the content of the composite theory proposed by the author into the framework of the Yukawa theory. We find several interesting relations between the coupling constants for meson-baryon interactions (valid in the global approximation). The classifications (in the global approximation) and the “G” transformations of the mesons and the baryons are introduced.