With the development of magneto-optical technology

the properties of the polaron in magnetic field have been of considerable interest.Larsen proposed a novel operator method to investigate the properties of 2D polarons.Peeters et al.discussed the properties of the magnetopolaron using the Feynmann path-integral approach.Wei and co-workers studied the induced potential and the self-energy of an interface magnetopolaron using the Green-function method.Huybrechts proposed a linear combination operator method

by which a strong coupling polaron was discussed.Later

many scholars studied the strong coupling polaron in many aspects by this method.The properties of the surface magnetopolaron have been discussed by the method of a linear combination operator and a perturbation by the present authors and co-werkers.In fact

the case of finite temperature is more significant.A lot of scholars studied the properties of the temperature of a polaron by a variety of different theoretical method.Saitok obtained that the effective mass of a polaron decreases with increasing temperature by means of the Feynmann path-integral approach.Many scholars got a alike conclusion also.This conclusion has been gained by the present authors and co-workers.However

Gu acquired an opposite result.Later

we studied the temperature dependence of the effective mass of the strong coupling magnetopolaron in polar crystals by means of the unitary transformation and an improved linear combination operator method again.The temperature characteristic of the effective mass was discussed in detail at different approximation calculation level.The result illustrated that the different approximation calculation level could provide two completely contrary conclusions on temperature depen-dence of the effective mass of the magnetopolaron.Using the different approximation calculation level

one can provide two complety contrary conclusions on temperature dependence of not only the effective mass of the magnetopolaron but also other of the mag-netopolaron.In this paper

the relationship between the mean number

n

of strong coupling magnetopolaron in polar crystal and magnetic field

B

and temperature

T

are studied by the method of the unitary transfor-mation and the linear combination operator.The magnetic field and temperature dependences of the mean number of the magnetopolaron are discussed in the different approximation calculation level.Numerical cal-culation for the RbCl crystal

as an example

are performed.The mean number of the magnetopolaron decreases with increasing temperature and increases with increasing magnetic field when the approximation calculation level is lower.The mean number of the magnetopolaron increases with increasing temperature and decreases with increasing magnetic field when the approximation calculation level is higher.