We calculate the lifetime of a surface plasmon on the surface of jellium metal from the process of the surface plasmon decaying into electron-hole pairs in the metal. We find that this process only occurs over a finite interval of wave vector, and at large values of wave vector. Our calculation contained two new features: (i) we used the Brillouin formula to normalize the electromagnetic field traveling along the surface, and (ii) we included the spin rotation term in the electron current. The latter contribution has no effect at large wave vector of the surface plasmon … ISSN 2469-9969 (online), 2469-9950 (print). ©2018 American Physical Society. All rights reserved. Physical Review B™ is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. The APS Physics logo and Physics logo are trademarks of the American Physical Society. Information about registration may …