In this paper the various properties of the rare-earth even-even nuclei (intrinsic excitation spectra, β-decay, and even-odd mass differences, etc.) are analysed with the new method presented in reference [10]. For this purpose, the single-particle levels have to be determined. It is found that on the basis of Nilsson's level scheme, with suitably chosen parameters μ and k, the spins and parities of the low-lying intrinsic spectra and the level spacing of odd-A nuclei may be explained, after taking account of the influence of pairing force. The parameters chosen are as follow: k～0.067-0.072, η～4-4.6　μ～0.59(N = 4), μ～0.45(N = 5) for proton　μ～0.40-0.45(N = 5), μ～0.33(N = 6) for neutron.　The variation of the energy eigenvalue induced by the change of parameter μ is estimated with the perturbation method, and the results are close to the exact eigenvalues. From the analyses of Er166, Er168, Yb170, Yb172, Yb174, Hf178, W182, Dy160 and Dy162 the following several conclusions may be drawn: 1. The majority of the low-lying intrinsic excited states of even-even nuclei may be considered as the pair-broken excited states. The calculated first pair-broken states, in spite of the large variation in their spins and parities, are observed in experiments systematically (Fig. 30). Their excitation energies range from 1.2 MeV to 1.6 MeV. The calculated variation of these energies with different nuclei agrees with experiments ap- proximately. These states correspond to the two quasi-particle excited states pointed out by Gallagher and Soloviev.2. Near the first pair-broken excited state, appears the Kπ=0+ pair excitation state. In Er166, Hf178 and W182 these pair excitation states have been observed (Fig. 32). In other nuclei, these pair excitation states have not been observed yet, because the β-decays from the neighbouring odd-odd nuclei to these states are highly forbidden or strictly forbidden. 3. The systematically occured Kπ = 2+ states (Fig. 31) in even-even nuclei (E～0.8-1.2 MeV) can not be considered as pair-broken excited states. Theoretically there does not exist in these nuclei (except Yb172) the Kπ= 2+ intrinsic state below 2 MeV.　4. The splittings in energy △E between the pair-broken doublets, K = |Ω1 ± Ω2|, vary violently with different nuclei and with different pair-broken states. △E～(40-700) KeV. 5. The variation of even-odd mass differences with different nuclei is analysed also and it is found that the even-odd mass difference depends sensitively on the single-particle level scheme. The fact that the calculated and the observed variation of even-odd mass differences agree with each other (Fig. 29) indicates that the single-particle level scheme determined in this paper is approximately correct. The average strength constant G deduced from the even-odd mass differences is close to that deduced from the energy spectra. In the calculation the cut-off energy C is chosen to be ≈ 4 MeV. (C》G). With increasing C the influences of the pairing force on the low-lying spectra may be compensated by decreasing the average strength constant G.