[Zhang, C. M.
; Wang, J.
; Zhao, Y. H.] Chinese Acad Sci, Natl Astron Observ, Beijing 100012, Peoples R China
; [Yin, H. X.] Shandong Univ, Sch Space Sci & Phys, Weihai 264209, Peoples R China
; [Song, L. M.] Chinese Acad Sci, Inst High Energy Phys, Astron Inst, Beijing 100039, Peoples R China
; [Menezes, D. P.] Univ Fed Santa Catarina, CFM, Dept Fis, BR-88040900 Florianopolis, SC, Brazil
; [Wickramasinghe, D. T.
; Ferrario, L.] Australian Natl Univ, Inst Math Sci, Canberra, ACT 0200, Australia
; [Chardonnet, P.] Univ Savoie, Lapth Lapp, F-74941 Annecy Le Vieux, France
We study the statistics of 61 measured masses of neutron stars (NSs) in binary pulsar systems, including 18 double NS (DNS) systems, 26 radio pulsars (10 in our Galaxy) with white dwarf (WD) companions, 3 NSs with main-sequence companions, 13 NSs in X-ray binaries, and one undetermined system. We derive a mean value of M = 1.46 +/- 0.30 M-circle dot. When the 46 NSs with measured spin periods are divided into two groups at 20 milliseconds, i.e., the millisecond pulsar (MSP) group and others, we find that their mass averages are, respectively, M = 1.57 +/- 0.35 M-circle dot and M = 1.37 +/- 0.23 M-circle dot. In the framework of the pulsar recycling hypothesis, this suggests that an accretion of approximately similar to 0.2 M-circle dot is sufficient to spin up a neutron star and place it in the millisecond pulsar group. Based on these estimates, an approximate empirical relation between the accreting mass (Lambda M) of recycled pulsar and its spin period is proposed as Delta M = 0.43 (M-circle dot)(P/1 ms)(-2/3). If we focus only on the DNS, the mass average of all 18 DNSs is 1.32 +/- 0.14 M-circle dot, and the mass averages of the recycled DNSs and the non-recycled NS companions are, respectively, 1.38 +/- 0.12 M-circle dot and 1.25 +/- 0.13 M-circle dot. This is consistent with the hypothesis that the masses of both NSs in DNS system have been affected by accretion. The mass average of MSPs is higher than the Chandrasekhar limit 1.44 M-circle dot, which may imply that most of binary MSPs form via the standard scenario by accretion recycling. If we were to assume that the mass of a MSP formed by the accretion induced collapse (AIC) of a white dwarf must be less than 1.35 M-circle dot, then the portion of the binary MSPs involved in the AICs would not be higher than 20%, which imposes a constraint on the AIC origin of MSPs. With accreting mass from the companion, the nuclear matter composition of MSP may experience a transition from the "soft" equation of state (EOS) to a "stiff" EOS or even neutron to quark matter.