# Effective-range expansion for two coupled channels and properties of bound states

## Abstract

The S matrix and the scattering-amplitude matrix (F matrix) are considered for the case of two coupled elastic-scattering channels differing by the values of the orbital angular momentum (l{sub 1} and l{sub 2} = l{sub 1} + 2). The matrix elements of the S and F matrices in the absence of Coulomb interaction are expressed in terms of the matrix elements of the matrix K{sup -1} inverse to the reaction K matrix. The elements of the K{sup -1} matrix are written in the form of expansions that are generalizations of the single-channel effective-range expansion. If there is a bound state in the system of colliding particles, then an analytic continuation of these expansions to the region of negative energies makes it possible to obtain both the position of the pole corresponding to this bound state and the residues of scattering amplitudes at this pole, the respective vertex constants and asymptotic normalization coefficients being expressed in terms of these residues. By way of example, the developed formalism is applied to describing triplet neutron-proton scattering.

- Authors:

- Moscow State University, Skobeltsyn Institute of Nuclear Physics (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22043893

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Atomic Nuclei

- Additional Journal Information:
- Journal Volume: 74; Journal Issue: 7; Other Information: Copyright (c) 2011 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7788

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ASYMPTOTIC SOLUTIONS; BOUND STATE; COUPLED CHANNEL THEORY; ELASTIC SCATTERING; K MATRIX; MATRIX ELEMENTS; ORBITAL ANGULAR MOMENTUM; PROTON-NEUTRON INTERACTIONS; S MATRIX; SCATTERING AMPLITUDES

### Citation Formats

```
Blokhintsev, L. D., E-mail: blokh@srd.sinp.msu.ru.
```*Effective-range expansion for two coupled channels and properties of bound states*. United States: N. p., 2011.
Web. doi:10.1134/S106377881105005X.

```
Blokhintsev, L. D., E-mail: blokh@srd.sinp.msu.ru.
```*Effective-range expansion for two coupled channels and properties of bound states*. United States. doi:10.1134/S106377881105005X.

```
Blokhintsev, L. D., E-mail: blokh@srd.sinp.msu.ru. Fri .
"Effective-range expansion for two coupled channels and properties of bound states". United States. doi:10.1134/S106377881105005X.
```

```
@article{osti_22043893,
```

title = {Effective-range expansion for two coupled channels and properties of bound states},

author = {Blokhintsev, L. D., E-mail: blokh@srd.sinp.msu.ru},

abstractNote = {The S matrix and the scattering-amplitude matrix (F matrix) are considered for the case of two coupled elastic-scattering channels differing by the values of the orbital angular momentum (l{sub 1} and l{sub 2} = l{sub 1} + 2). The matrix elements of the S and F matrices in the absence of Coulomb interaction are expressed in terms of the matrix elements of the matrix K{sup -1} inverse to the reaction K matrix. The elements of the K{sup -1} matrix are written in the form of expansions that are generalizations of the single-channel effective-range expansion. If there is a bound state in the system of colliding particles, then an analytic continuation of these expansions to the region of negative energies makes it possible to obtain both the position of the pole corresponding to this bound state and the residues of scattering amplitudes at this pole, the respective vertex constants and asymptotic normalization coefficients being expressed in terms of these residues. By way of example, the developed formalism is applied to describing triplet neutron-proton scattering.},

doi = {10.1134/S106377881105005X},

journal = {Physics of Atomic Nuclei},

issn = {1063-7788},

number = 7,

volume = 74,

place = {United States},

year = {2011},

month = {7}

}