In recent years

the problem of a magnetopolaron has been of considerable interest.Larsen proposed a fourth-order perturbation method to calculate the ground state energy of two-dimensional polaron in a magnetic field.Employing Haga’s perturbation method

Ze

et al

.derived an effective Hamiltonian for the interface magnetopolaron in polar crystals at zero temperature

in which the interactions of both bulk LO phonons and interface phonons have been taken into account.Using the Green’s function method

Wei

et al

studied the cyclotron resonance mass of an electron interacting with bulk longitudinal optical(BO)phonons as well as surface optical(SO)phonons in a polar crystals slab at finite temperature and found that the temperature dependence of magnetopolaron depends strongly on the strength of the magnetic field.Wang

et al

investigated the magnetic field and temperature dependence of the properties of a magnetopolaron at the interface of polar-polar crystals in an external magnetic field by using the generalized Haga perturbation method.By using variational method of Pekar type

Zhou and co-workers studied the energy levels of strong coupling magnetopolaron in disk-shape quantum dot(QD)and quantum well(QW).Madkour

et al

. studied the effect of magnetic field on surface polaron states in a polar crystal interface and emphasized the result that the presence of magnetic field leads to a local potential for charge carriers at the interface.Based on Wigner-Brillouin theory

D.E.N.Brancus and G.Stan investigated the state energy of an anisotropic three-dimensional polaron in a magnetica field.One of our authors have done a lot of works on the proterties of the surface magnetopolaron.The properties of surface polaron in a magnetic field have been further discussed by the present authors and co-workers.Tokuda studied the property of the mean number of the optical and the piezoelectric polarons and the mean number of the acoustic and optical polarons via deformation potential by using improved variational method.However

the mean number of optical phonon of surface magnetopolarons at finite temperature has not been studied so far.In this paper

the properties of surface magnetopolaron which is a strong

weak-coupling of optical phonon was discussed by using Tokuda’s improved linear combination operator

the unitry transformation and the Lagrange multiplier methods.The mean number of optical phonons of the strong

weak-coupling magnetopolaron are calculated.Numerical calculations for KCl crystals

as an example

are performed.The relation of the vibration frequency and the mean number of optical phonons to magnetic field B

temperature T and Lagrange multiplier u are discussed.The result illustrates that the vibration frequency λ of surface magnetopolaron will increase with increasing magnetic field

B

temperature

T

and Lagrange multiplier

u

;the mean number of optical phonons will increase with increasing

B

T

and

u

.