The alkali metals all have the same crystal structure (body-centred cubic) and thus the only relevant factors are the number of atoms that can fit into a certain volume and the mass of one of the atoms, since density is defined as mass per unit volume.
ðɪ ˈælkəlˌaɪ mˈɛɾəlz ˈɔːl hæv ðə sˈeɪm kɹˈɪstəl stɹˈʌktʃɚ bˈɑːdisˈɛntəd kjˈuːbɪk ænd ðˈʌs ðɪ ˈoʊnli ɹˈɛlᵻvənt fˈæktɚz ɑːɹ ðə nˈʌmbɚɹ ʌv ˈæɾəmz ðæt kæn fˈɪt ˌɪntʊ ɐ sˈɜːʔn̩ vˈɑːljuːm ænd ðə mˈæs ʌv wˈʌn ʌvðɪ ˈæɾəmz, sˈɪns dˈɛnsᵻɾi ɪz dᵻfˈaɪnd æz mˈæs pɜː jˈuːnɪt vˈɑːljuːm.