The pulsational properties of RR Lyrae variables of galactic globular clusters (GGCs) provide an unique opportunity for testing the structural parameters of pulsating stars and the prescriptions of stellar evolutionary theories. According to such an evidence, in the last decades the well known van Albada & Baker (1971) relation connecting the pulsation periods to stellar masses, luminosities and effective temperatures has been at the basis of several investigations on the evolutionary status of HB stars, raising in particular a well known debate about the actual luminosity of RR Lyrae pulsators.
A relevant point to remember is that pulsational periods are unaffected either by interstellar reddening or by the distance modulus and thus provide firm and accurate observational data which unambiguously constrain the evolutionary parameters of the evolving variables. However, the pulsational phenomenon provides a further relevant observable, namely the amplitude of the luminosity variation. According to such plain evidence, as early as the beginning of the century Bailey (1899, 1902) investigated the properties of RR Lyrae pulsators in the period-amplitude diagram which is now usually named after its inventor.
However, the investigation of pulsational properties in the Bailey diagram has never gone beyond an empirical and qualitative approach. For instance, we know that along this diagram the RR Lyrae variables of different Oosterhoff types show different distributions, but until recently we have been unable to investigate the origin of such a behavior because we lack a detailed theoretical scenario connecting pulsational amplitudes with the structural parameters of the pulsating stars. This is due to the fact that periods can be easily derived by a simple linear and adiabatic approach to the pulsational phenomenon, i.e. the canonical von Ritter relation, whereas the amplitudes are the result of detailed nonlinear investigations which require a much more difficult theoretical and computational effort.
To address this problem properly, during the last few years we have undertaken a theoretical project aimed at the evaluation of the pulsational amplitudes and the modal stability of RR Lyrae variables by computing a large and homogeneous set of nonlinear and time-dependent convective envelope models. The primary goal of this approach is to provide, for the first time, a sound theoretical scenario of the dependence of all the pulsational observables on astrophysical parameters such as stellar mass and chemical composition. Moreover, the pulsation properties of nonlinear RR Lyrae models, when evaluated at full amplitude, can supply useful suggestions concerning the physical processes which drive and/or quench the pulsations mechanism.
Bono & Stellingwerf (1994, hereinafter referred to as BS) have already shown that a nonlinear approach is necessary for an accurate determination of periods. The outcome was similar for properly locating the instability regions into the HR diagram. Indeed, the nonlinear instability boundaries of fundamental (F) and first overtone (FO) pulsators have been already found in substantial agreement with the observed color distribution of RR Lyrae variables in selected galactic globulars (Bono et al. 1995, hereinafter referred to as BCM). Moreover, the minimum fundamentalized periods of RR pulsators belonging both to Oosterhoff I (OoI) and Oosterhoff II (OoII) globular clusters have been explained by taking simultaneously into account the evolutionary history and the modal stability of variable stars in the instability strip (Bono et al. 1995).
The results presented in this paper have been obtained by using the same theoretical framework adopted by Bono & Stellingwerf (1992) and BS in the first two papers of this series. Physical assumptions and numerical procedures have been already described in the quoted papers and in Stellingwerf (1975, 1982). The reader is referred to these papers for a detailed description. The main differences between the present investigation and the results obtained by BS are:
1) the RR Lyrae models supplied by BS were computed by assuming a fixed
mass value (M=0.65 
) whereas in the present paper three
different mass values have been adopted (M=0.58, 0.65, 0.75 
)
which cover the whole expected range of HB stars.
2) In order to compare the pulsation properties of RR Lyrae models with
previous theoretical works, BS adopted a helium abundance by mass of Y=0.30
whereas all the present computations have been performed by adopting a
helium content of Y=0.24.
We chose this value since on the basis of both the R (or R') method
(Buzzoni et al. 1983) and the determination of the ratio He/H in
HII regions and planetary nebulae (Peimbert & Torres-Peimbert 1976;
Peimbert 1995 and references therein)
there is a general consensus on the fact that a suitable range for the
helium abundance of population II stars belonging to GGCs is
(Pagel 1995 and references therein).
Owing to the marginal dependence of the pulsational properties of metal poor stars on metal content (Christy 1966), a fixed metal abundance, Z=0.0001, has been adopted. However, it is worth underlining that throughout the pulsation cycle the transformation of luminosity and temperature into the observational plane depends on the metal content, since both bolometric correction and color-temperature relation present a non negligible dependence on such a parameter.
According to theoretical expectations (see, e.g.,
Castellani et al. 1989, hereinafter referred to as CCP)
we investigated the pulsational behavior of cluster variables
by assuming two different stellar masses for properly covering
the range of pulsator masses expected in clusters with ``solar scaled"
metallicities 
(
) and
(
).
In order to account for the suggested overabundance of alpha-elements,
which would produce
an increase in the ``effective metallicity" (Straniero & Chieffi
1991) and a further decrease in the pulsator masses, a set of models
characterized by a smaller mass value, 
,
was also computed.
According to CCP, this pulsator mass corresponds to a cluster effective
metallicity
. This value can be obtained by increasing, in a solar
scaled metallicity of Z=0.001, the amount of alpha-elements
of a factor roughly equal to 9 (see Salaris et al. 1991).
In the following section we provide an atlas of selected theoretical light curves arranged according to the effective temperature and the luminosity of each model. In Sect. 3 nonlinear periods are compared to the periods obtained by using the van Albada & Baker (1971) relations. In order to accomplish a comparison with observational data from RR Lyrae stars belonging to GGCs, the results of pulsation theory will be connected with the canonical HB evolutionary scenario.
Section 4 deals with the pulsational amplitude as a function of effective temperature, luminosity and mass. These results are collected in Sect. 5 for providing a theoretical Bailey diagram which is examined in terms of evolutionary expectations. In Sect. 6 this theoretical scenario is compared with observational evidences from RR Lyrae pulsators in selected GGCs. A final discussion about some residual but relevant mismatches between theory and observations closes the paper.