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This interesting pure number is the rest energy of X divided by the gravitational attraction of two protons separated by the Compton wavelength of X, where X is anything. The mass M o corresponding to the reduced quantity M o is (taking a ::::: 1): 8 _ M o = 9'7T mpMo ::::: 10 g::::: M 0 (11.56)

Hence it is valid for M near Mo. Our model yields the remarkable prediction that no white dwarf star can have a mass larger than M o, because otherwise (11.53) would give an imaginary radius. The physical reason underlying this result is that if the mass is greater than a certain amount, the pressure coming from the Pauli exclusion principle is not sufficient to support the gas against gravitational collapse. The radius-mass relationship of a white dwarf star, according to our model, has the form shown in Fig. 11.6, where the solid lines indicate the regions covered by formulas (11.51) and (11.53). We have not been able to calculate a, so that an exact value of M o cannot be obtained. More refined considerations* give the result M o = 1.4M0 (11.57) This mass is known as the Chandrasekhar limit. Thus according to our model no star can become a white dwarf unless its mass is less than 1.4M0 . This conclusion has so far been verified by astronomical observations. If the mass of a star is greater than the Chandrasekhar limit then it will eventually collapse under its own gravitational attraction. When the density becomes so high that new interactions, dormant thus far, are awakened, a new regime takes over. For example, the star could explode as a supernova.

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11.3 LANDAU DIAMAGNETISM Van Leeuwen's theoremt states that the phenomenon of diamagnetism is absent in classical statistical mechanics. Landau first showed how diamagnetism arises from the quantization of the orbits of charged particles in a magnetic field. The magnetic susceptibility per unit volume of a system is defined to be 8v1t X == (11.58)

S. Chandrasekhar, Stellar Structure (Dover, New York, 1957), XI. tSee Problem 8.7. *L. Landau, Z. Phys. 64,629 (1930).

where Jt is the average induced magnetic moment per unit volume of the system along the direction of an external magnetic field H:

(11.59)

where Yl' is the Hamiltonian of the system in the presence of an external magnetic field H. For weak. fields the Hamiltonian Yl'depends on H linearly. In the canonical ensemble we have

FIGURE 5.4 Symbol ESRX crosses beneath the moving average early in March and starts falling in earnest by late April.

You can use a query to extract information that you want to view in a database. Queries are especially useful when you want to glean data from multiple tables. Queries are similar to filters but offer you greater control when it comes to viewing records. You can use the Query Wizard to help you select what fields you want to include in the analysis. There are several types of Query Wizard. These include Simple, which is covered here; Crosstab, to display information in a spreadsheet-like format; Find Duplicates, to find records with duplicate field values; and Find Unmatched, to find records in one table with no related records in another table.

(11.60)

Jt= kT!-(log2)

(11.61)

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