Table 1 Literature values for the electron–electron and electron–phonon interaction strengths, β_ee and γ_ep, of various metals.

Metal	λ〈ω²〉 (meV²/ħ²)	Θ_D (K)	τ_ep (fs)	\(\gamma _{{\mathrm{ep}}}^{ - 1}\) (fs)	\(\beta _{{\mathrm{ee}}}^{ - 1}\) (fs)	τ_E (fs)	τ_H(fs)
Li	160	340	12	110	55	230	11
Na	13	158	29	1400	34	1600	7
K	3.4	91	37	5200	20	5500	4
Rb	1.8	56	27	9900	17	1.0 × 10⁴	3
Cs	0.85	38	25	2.1 × 10⁴	14	2.1 × 10⁴	3
Ta	190	240	4.6	93	17	150
Mo	240	450	13	74	57	170
Fe	280	470	12	63	7.5	92
Rh	350	480	10	51	12	89
Ni	230	450	13	77	14	120
Pd	130	270	8.6	140	8	170
Pt	140	240	6.1	100	8	160
Cu	57	340	31	310	160	650	30
Ag	23	230	34	790	300	1500	60
Au	15	170	27	1200	300	2100	60
Al	270	430	10	67	40	150	8
Gd	90	200	7	200	28	290
Tb	90	200	7	200	18	270

We use the electron-electron and electron interaction strengths to calculate τ_H, the time-scale high energy electronic states remain occupied for, and τ_E, the time-scale for energy transfer between the electronic subsystem and lattice. The values for the second frequency moment of the Eliashberg function λ〈ω²〉 and Debye temperature Θ_D are from Allen⁵⁹, Kittel⁶¹, and Papaconstantopoulos et al.⁶². To highlight the large discrepancy between electron–phonon quasiparticle scattering time τ_ep and time-scales τ_H and τ_E, we show \(\tau _{{\mathrm{ep}}} \approx \hbar /\left( {2\pi \lambda k_{\mathrm{B}}T} \right)\) for each metal. However, we emphasize that τ_ep is not an input into our model. The values for \(\beta _{{\mathrm{ee}}}^{ - 1}\) for the alkali metals are predictions from Fermi-liquid theory for a homogenous electron gas³². The values for \(\beta _{{\mathrm{ee}}}^{ - 1}\) of other metals are from two photon photoemission data³², except for Pt. We assume \(\beta _{{\mathrm{ee}}}^{ - 1}\) for Pt is equal to \(\beta _{{\mathrm{ee}}}^{ - 1}\) for Pd.

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