Jones wants England to seize 'greatness'
Jonathan Joseph scored a hat-trick as England ran in seven tries, with Owen Farrell overcoming a leg injury to kick 26 points as they overpowered Scotland in posting a record score in the 135th edition of rugby union's oldest international fixture.
Victory also saw England equal New Zealand's record of 18 successive Test wins by a leading nation.
England will break the world champions' mark if they beat Ireland in Dublin next weekend, where a win would also see them complete a second straight clean sweep in the Six Nations.
No side has done that in the Six Nations era, with France achieving consecutive Five Nations Grand Slams in 1997 and 1998.
England last managed the feat in 1992 and 1993
"We've got a fantastic opportunity," said Jones, yet to lose a match as England coach since taking charge following the hosts' first-round exit at the 2015 World Cup.
"It [would] mean for the players they've achieved greatness," the Australian added.
"How many times in your life do you get to be great? It's exciting. They're in the dressing room now talking about it. They want to do it."
Next Saturday's match takes place on St Patrick's weekend, with Ireland looking to bounce back from a 22-9 loss to Wales in Cardiff on Friday.
Jones said Ireland, who ended New Zealand's winning streak, would love nothing more than to spoil England's party.
"Ireland, psychologically, are in a very strong position," he added.
"They're beaten, they're out of the tournament and they love spoiling parties.
"And the party they'd love to spoil the most is the England party," insisted Jones, coach of the Australia side beaten by England in the 2003 World Cup final
"We're vulnerable, because we've won, we're champions of the Six Nations.
"We're going to have to work really hard to get ourselves right for the game. And we will."
Having established a 30-7 lead at half-time, England didn't let up and added 31 more points after the break on Saturday.
"The number one team in the world goes on and finishes that off," added Jones, whose ultimate ambition with England is to dethrone the All Blacks by winning the 2019 World Cup in Japan.
"We're not beating our chests and saying we're the number one team in the world, but we aspire to be the number one team in the world."
Scotland kicked off one win away from a Triple Crown and with high hopes of a first victory at Twickenham since 1983.
But they were never in the game, with their wafer-thin defence repeatedly ripped apart.
However, a win over Italy at Murrayfield next weekend could still see them finish second for the first time since the tournament became the Six Nations.
That would be a fitting way for Scotland to see off coach Vern Cotter.
The New Zealander is leaving to join French club Montpellier after Scotland felt they had to get Glasgow boss Gregor Townsend – 10 of whose players were in the starting XV at Twickenham – on board as coach of the national side or risk losing him to an overseas offer.
"It just got away from us quite quickly," said the understated Cotter.
Scotland captain John Barclay was rather more blunt, saying: "We just didn't show up today…That was useless."
A bruising encounter saw England's Elliot Daly and Scotland's Stuart Hogg, Tommy Seymour and Ryan Wilson all exit early with head injuries – a worrying sign given rugby union's growing number of concussions.
"It is a contact sport," said Cotter. "That's why the players play it – they enjoy the contact.
"Some days you have them [head injuries] and some days you have more of them," he added.
Agence France-Presse
