Majorana interaction

Figure 5.5 Splitting of the degenerate C-H stretching modes of acetylene due to the Majorana interaction, M12.

The effect of neutron-proton symmetry breaking on the distribution of M1 strength in the SU(3) limit of the Interacting Boson Model (IBA-2) is studied. A possible alternative choice for the Majorana force is investigated, with a structure that resembles more closely that which is calculated in microscopic theories. It is found that the specific choice for the Majorana interaction has important consequences for the magnetic strength distribution function. In addition it allows for an alternative interpretation of the second excited K7T=0+ band in rare earth nuclei, as a mixed-symmetry state. 

Another important difference between the two choices for the Majorana interaction shows up in the calculated M1 strength distribution. In the IBA-2 model, the M1 transition operator is written as... 

It is then possible, by proper adjustments of the Fermi parameter/12, to calibrate both the energy position and the amount of wavefunction mixing against the experimental values. The Fermi operator introduced here is a special case of Majorana interaction, which can readily be generalized to higher polyads of vibrational levels. 

Crystal anapole moment is composed of the atomic magnetic moments which array in anapole structure [3]. It has the same intrinsic structure as Majorana neutrino [2], If we plant a p decay atom into this anapole lattice, the crystal anapole moment will couple to the nuclear anapole moment of the decaying nuclei. So the emitted electron will be given an additional pseudoscalar interaction by the presence of the crystal anapole moment. Then the emission probability will be increased. This is a similar process to that assumed by Zel dovich [1], The variation of the decay rate may be measured to tell whether the crystal anapole moment has an effect on the p decay or not. 

As the anapole interaction is the candidate which directly breaks parity conservation in electromagnetic interaction [1], it is very desirable to test whether the anapole moment could couple to the p decay or not. This experiment can be performed by solid state detectors as well asby a magnetic spectrometer. There are also other choices for the crystal samples [3] and p sources. Since the anapole moment has the same intrinsic structure as for Majorana neutrinos, its coupling is valid to both p decay and p+ decay. 

It is instructive to analyze the effect of the interaction terms (Majorana operators) in Eq. (6.24). These terms split the degeneracies of the multiplets of Figure 6.1, as shown in Figure 6.3. Thus, the Majorana terms remove the degeneracies of the local modes and bring the behavior of the molecule towards the normal limit, precisely in the same way as in tri- or tetratomic molecules. 

Once this calculation is completed, one can then examine each spectral region bounded by intervals of energy of the order of AE = 100 cm-1 and couple the states of a given species that fall into that region. Table 6.7 shows, for example, states up to three quanta of vibration of total species E]u that fall in the region 5950-6050 cm-1. These states are subsequently coupled by residual interblock interactions of the Majorana type [Eq. (6.16)]. A complete account of this type of calculations is given in Iachello and Oss (1993). 

WIGNER FORCE. Short-range nuclear force of noncxchangc type postulated phenomenologically as pait of the interaction between nucleons. Postulated exchange forces are Bartlett, Heisenberg, and Majorana forces. 

In the IBA-2 model [Ari83] the structure of the collective states in even-even nuclei is calculated by considering a system of interacting neutron and proton s and d bosons. We will focus attention on the Majorana force,... 

Fig. 10. Muonium-antimuonium conversion in theories beyond the standard model. The interaction could be mediated by (a) a doubly charged Higgs boson A++ [52,53], (b) heavy Majorana neutrinos [52], (c) a neutral scalar [54], e.g. a supersymmetric r-sneutrino vT [55,56], or (d) a bileptonic gauge boson X++ [57]...

These matrix elements can also be written in the local basis v v ). For this purpose it is convenient to introduce a slightly different form of the interaction term, often referred to as the Majorana operator, Mi2-> which is related to Cu (2) h 2 by means of several conventions. We choose to define Mjj such that in place of (2.45), we obtain the following matrix elements ... 

Figure 29. Different blocking forms of the Hamiltonian matrix corresponding to the Majorana left side) and Fermi 2 1 interaction (right side). Off-diagonal matrix elements of the Majorana operator are denoted by circles, crosses refer to the Fermi interaction.

Although we will not discuss in detail this particular aspect of anharmonic resonances, it is important to note that Darling-Dennison couplings are automatically included by the action of the Majorana operator. A practical way to convince ourselves of this inclusion is to diagonalize (either numerically or in closed form) the Hamiltonian matrix explicitly for the first two polyads of levels and then to convert, in normal-mode notation, the vibrational states obtained. As discussed in Ref. 11, the Hamiltonian (4.38) can also be written (neglecting Cj2 and Cj2 interactions) as... 

With the local basis, we are ready to construct a triatomic-like Hamiltonian operator where most of the physically relevant interactions should be either diagonal or in the nondiagonal form of the Majorana operator. This is a direct consequence of our choice for the coupling scheme (1 -I- 2) -f- 3, which is, in fact, done to favor interactions of the type (H-2). So for a linear tetratomic molecule we write the following Hamiltonian operator ... 

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